{"id":14716,"date":"2023-06-12T08:41:22","date_gmt":"2023-06-11T23:41:22","guid":{"rendered":"https:\/\/zelkova-tree.net\/WordPress\/?p=14716"},"modified":"2023-06-12T09:00:18","modified_gmt":"2023-06-12T00:00:18","slug":"%e3%81%8c%e3%82%92%e5%89%b2%e3%82%8a%e5%88%87%e3%82%8b%e3%81%a8%e3%81%84%e3%81%86%e3%81%ae%e3%81%af%e5%ae%9a%e7%90%86%e3%81%a7%e3%81%af%e3%81%aa%e3%81%84","status":"publish","type":"post","link":"https:\/\/zelkova-tree.net\/WordPress\/2023\/06\/12\/%e3%81%8c%e3%82%92%e5%89%b2%e3%82%8a%e5%88%87%e3%82%8b%e3%81%a8%e3%81%84%e3%81%86%e3%81%ae%e3%81%af%e5%ae%9a%e7%90%86%e3%81%a7%e3%81%af%e3%81%aa%e3%81%84\/","title":{"rendered":"ψ\u304cφ\u3092\u5272\u308a\u5207\u308b\u3068\u3044\u3046\u306e\u306f\u5b9a\u7406\u3067\u306f\u306a\u3044"},"content":{"rendered":"

<\/p>\n

Get\u03c8\u95a2\u6570\u306e\u4ed5\u69d8\u3092\u518d\u8003\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\uff0e\u03c8\u6570\u306f\uff4e\u3068K\u306b\u3088\u3063\u3066\u6c7a\u307e\u308b\u304c\uff0c\u03c8\u6570\u304c\u6c7a\u5b9a\u3067\u304d\u306a\u3044\u5834\u5408\u3082\u3042\u308b\uff0e\u03c8\u6570\u304c\u5f97\u3089\u308c\u308b\u6761\u4ef6\u306fN\u306e\u3079\u304d\u5270\u4f59\u6570\u5217\u306e\u4e2d\uff08\u7d42\u7aef\uff09\u306b\uff11\u304c\u73fe\u308c\u308b\u3053\u3068\u3060\u304c\uff0c\u5270\u4f59\u6570\u5217\u306b\uff11\u304c\u5165\u3089\u306a\u3044\u5834\u5408\u306f\u3044\u304f\u3089\u3067\u3082\u3042\u308b\uff0e\u3053\u306e\u3088\u3046\u306a\u3068\u304d\u306b\uff0c\u03c8\u6570\u306e\u5b9a\u7fa9\u306b\u5f93\u3063\u3066\uff0c\uff4e\u306b\u5bfe\u5fdc\u3057\u305fK\u306e\u6700\u5c0f\u306e\u5024\u3092\u6c7a\u5b9a\u3059\u308b\u3068\u3044\u3046\u306e\u304cGet\u03c8\u95a2\u6570\u306e\u5f79\u5272\u3060\u304c\uff0c\u305d\u306e\u52d5\u4f5c\u306b\u306f\u304b\u306a\u308a\u7591\u554f\u304c\u3042\u308b\uff0e\u2460\u9078\u3070\u308c\u308bK\u304c\u6975\u7aef\u306b\u5c0f\u3055\u3044\uff0e\u307b\u3068\u3093\u3069\u306f1, 2, \uff13, 5 \u306e\u3044\u305a\u308c\u304b\u3060\uff0e\u2461\u8a2d\u5b9a\u5024\u3067\u3059\u3067\u306b\u03c8\u6570\u304c\u78ba\u5b9a\u3057\u3066\u3044\u308b\u306e\u306b\uff0c\u30dc\u30bf\u30f3\u3092\u62bc\u3055\u308c\u308b\u3068\u3088\u308a\u5c0f\u3055\u3044\u5024\u3092\u63a2\u3057\u3066\u63d0\u793a\u3059\u308b\u3068\u3044\u3046\u52d5\u4f5c\u306b\u306a\u3063\u3066\u3044\u308b\uff0e<\/p>\n

\u9069\u5408\u3059\u308bK\u3092\uff11\u304b\u3089\u63a2\u3059\u306e\u3067\u306f\u306a\u304f\uff0c\u76f4\u8fd1\u306eK'<K\u3092\u6c42\u3081\u308b\u3068\u3044\u3046\u306e\u304c\u9069\u5f53\u3067\u306f\u306a\u3044\u3060\u308d\u3046\u304b\uff1f\u9006\u306b\uff0bK\u306e\u65b9\u3092\u63a2\u3059\u3068\u3044\u3046\u3053\u3068\u3082\u8003\u3048\u3089\u308c\u308b\u304c\uff0c\u5c0f\u3055\u3044\u65b9\u3092\u63a2\u3059\u3068\u3044\u3046\u306e\u304c\u81ea\u7136\u3060\u308d\u3046\uff0e\u3069\u306e\u3088\u3046\u306aN\u306b\u5bfe\u3057\u3066\u3082\uff0cK=1, 2, \uff13, 5\u306e\u3044\u305a\u308c\u304b\u306f\u5fc5\u305a\u03c8\u5024\u3092\u4e0e\u3048\u308b\u3068\u8a00\u3048\u308b\u3060\u308d\u3046\u304b\uff1f<\/strong>\u3053\u308c\u306f\u4e88\u60f3\u554f\u984c\u3068\u3057\u3066\u7acb\u3066\u3066\u304a\u3044\u3066\u3082\u3088\u3044\u304b\u3082\u3057\u308c\u306a\u3044\uff0e<\/p>\n

\u25b2<\/font>PsiFunction\u306f\u305d\u306e\u4e2d\u3067\u8868\u793a\u51fa\u529b\u3057\u3066\u3044\u308b\uff0e\u21d2\u3044\u3084\uff0cK\u306e\u5024\u3092\u5909\u3048\u305f\u3068\u304d\u306bValueChanged\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u751f\u3057\u3066\u3044\u308b\u306e\u3060\u308d\u3046\uff0e\u21d2passflag\u3092\u4f7f\u3063\u3066\u51fa\u529b\u3092\u6291\u5236\u3059\u308b\u3088\u3046\u306b\u3057\u305f\uff0e<\/p>\n

\u03c8\u6570\u304c\u6c42\u3081\u3089\u308c\u308b\u6761\u4ef6\u3068\u3057\u3066\u300cN\u3068K\u304c\u4e92\u3044\u306b\u7d20\u300d\u3068\u3044\u3046\u306e\u304c\u9069\u7528\u3055\u308c\u3066\u3044\u308b\uff0e\u3053\u308c\u306f\u6b63\u3057\u3044\u3068\u8a00\u3048\u308b\u304b\uff1f\u21d2EFA\u306e\u5b9a\u7fa9\u8868\u306b\u3082\u305d\u3046\u66f8\u3044\u3066\u3042\u308b\u306e\u3067\u9593\u9055\u3044\u306a\u3044\u3060\u308d\u3046\uff0e<\/p>\n

\u25b2<\/font>N=10, K=1234567\u3067\u30cf\u30f3\u30b0\u3057\u3066\u3057\u307e\u3063\u305f\uff0e\u21d2MakeStripePattern\u3067\u624b\u9593\u53d6\u3063\u3066\u3044\u308b\uff0e\u6587\u5b57\u5217\u306e\u9577\u3055\u3092\u5236\u9650\u3057\u3066\u3044\u306a\u3044\u306e\u3067\u7121\u95c7\u306b\u9577\u3044\u30c6\u30ad\u30b9\u30c8\u3092\u751f\u6210\u3057\u3088\u3046\u3068\u3057\u3066\u3044\u308b\uff0e\u21d2MaxOutput=10000\u3067\u6253\u3061\u5207\u308b\u3088\u3046\u306b\u3057\u305f\uff0e\u21d2\u52d5\u4f5c\u3059\u308b\u3088\u3046\u306b\u306a\u3063\u305f\uff0e<\/p>\n

\u03c8(n, K)\u3068\u3044\u3046\u95a2\u6570\u306f\u5143\u3005\u5faa\u74b0\u5c0f\u6570\u306b\u95a2\u3059\u308b\u8b70\u8ad6\u306e\u4e2d\u3067\u63d0\u6848\u3055\u308c\u305f\u3082\u306e\u3067\u3042\u308a\uff0c\u305d\u3053\u3067\u306fu-length function\u3068\u547c\u3070\u308c\u3066\u3044\u308b\uff0eu-length\u3068\u306f\uff4e\u306e\u5faa\u74b0\u7bc0\u306e\u9577\u3055\u3067\u3042\u308a\uff0c\uff20\u3068\u8868\u8a18\u3055\u308c\u3066\u3044\u308b\u5024\u3067\u3042\u308b\uff0e\u5f93\u3063\u3066\uff0cEFA\u306e\u8a18\u8ff0\u304c\u6b63\u3057\u3044\u3068\u3059\u308c\u3070\uff0cu-length=\u03c8(n,B)\u3067\u8a08\u7b97\u3067\u304d\u306a\u304f\u3066\u306f\u306a\u3089\u306a\u3044\uff0en=123, B=10\u306e\u3068\u304d\uff0c@=5\u3067nU=99999\u3068\u306a\u308b\uff0e\u3053\u306e\u3068\u304d, N=10, K=123\u3067\u5270\u4f59\u6570\u5217\u3092\u8a08\u7b97\u3059\u308b\u3068#=5\u3068\u306a\u3063\u3066\uff20\u306e\u5024\u3068\u4e00\u81f4\u3059\u308b\uff0e\u305f\u3060\u3057\uff0c\u03c8\u5024\u306f\u4e0d\u5b9a\u306e\u307e\u307e\u3060\uff0e<\/p>\n

n*U(b,n) = r*(by<\/big>(b,n)<\/sup>-1)\u306e\u3088\u3046\u306a\u95a2\u4fc2\u5f0f\u304c\u63d0\u793a\u3055\u308c\u3066\u3044\u308b\uff0eU(b,n)\u306f\u300c\u5faa\u74b0\u5358\u4f4d\u300d\u3068\u547c\u3070\u308c\u308b\u6574\u6570\u5024\u3067\u73fe\u884c\u30c4\u30fc\u30eb\u306eU\u3068\u4e00\u81f4\u3059\u308b\uff0e\u4e0a\u5f0f\u306e\u5de6\u8fba\u306fnU\u3068\u547c\u3093\u3067\u3044\u308b\u3082\u306e\u306b\u4ed6\u306a\u3089\u306a\u3044\u304b\u3089\uff0c\u3053\u306e\u5024\u304c\u53f3\u8fba\u5f0f\u306e\u3088\u3046\u306b\u5206\u89e3\u3067\u304d\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u304b\u3081\u306a\u304f\u3066\u306f\u306a\u3089\u306a\u3044\uff0e<\/p>\n

\u25b2<\/font>N\u306e\u5165\u529b\u5024\u304cMAX_INT64\u3092\u8d85\u3048\u3066\u3044\u308b\u3068\u304d\uff0c\u9ed9\u3063\u3066\u5143\u306e\u5024\u306b\u623b\u3057\u3066\u3044\u308b\uff0e\u21d2\u30d1\u30fc\u30c4\u304c\u4e0a\u9650\u3092\u8d85\u3048\u308b\u5024\u3092\u62d2\u5426\u3057\u3066\u3044\u308b\u305f\u3081\u3067\u306f\u306a\u3044\u304b\uff1f<\/p>\n

EFA\u306b\u8a18\u8f09\u3055\u308c\u305f\u4e8b\u4f8b\u3092\u691c\u8a0e\u3057\u3066\u307f\u3088\u3046\uff0e<\/p>\n

\u2026 given n=21, you easily find out the remainder sequence {1,10,16,13,4,19,1,..}, while u-length function y<\/big>(10,21)=6, U(10,21)=47619 and r=1. However if you take U=47619*x and r=x, then the equation holds for any x. <\/em><\/p>\n

n=21, B=10\u3068\u3059\u308b\u3068\uff0cU=47619, nU=999999 \u3067 @=6\uff0er=1 \u3067\u3042\u308b\u304b\u3069\u3046\u304b\u306f\u753b\u9762\u3067\u306f\u5206\u304b\u3089\u306a\u3044\uff0e\u21d2 nB=n%B \u3068\u3044\u3046\u5024\u3082\u8868\u793a\u3055\u308c\u3066\u3088\u3044\u304b\u3082\u3057\u308c\u306a\u3044\uff0e\u591a\u5206 r=n%B\u306e\u306f\u305a\u3060\uff0e\u4e00\u65b9\uff0cn=10, K=21\u3068\u3044\u3046\u8a2d\u5b9a\u3067\u306f\uff0c#=6\u3067 cycle={10,16,13,4,19,1,10,}\u304c\u8868\u793a\u3055\u308c\u308b\uff0e\u305f\u3060\u3057\uff0c\u03c8\u306f\u7a7a\u6b04\u306b\u306a\u3063\u3066\u3044\u308b\uff0e\u3064\u307e\u308a\uff0c\uff4e\u306b\u3042\u308b\u5024\u3092\u8a2d\u5b9a\u3057\uff0cK\u3068B\u306b\u540c\u3058\u5024\u3092\u4ee3\u5165\u3059\u308b\u3068\uff0c\u4e0a\u306e\u72b6\u6cc1\u3092\u518d\u73fe\u3067\u304d\u308b\uff0e\u3044\u3084\uff0c\u9055\u3046\uff0e\u3079\u304d\u5270\u4f59\u753b\u9762\u3067\u306f B\u2192n, n\u2192K \u306e\u3088\u3046\u306b\u8a2d\u5b9a\u3057\u306a\u304f\u3066\u306f\u306a\u3089\u306a\u3044\uff0e<\/p>\n

\u3053\u306e\uff12\u3064\u306e\u9006\u5411\u304d\u306e\u8a08\u7b97\u3092\u4e00\u753b\u9762\u306b\u540c\u6642\u306b\u8868\u793a\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u308b\u3060\u308d\u3046\u304b\uff1f\uff4e\u304c\u9664\u6570K\u306b\u5411\u304b\u3046\u3068\u3053\u308d\u304c\u96e3\u89e3\u306a\u3068\u3053\u308d\u3060\uff0e\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u540d\u524d\u304c\u8aa4\u89e3\u3092\u62db\u304d\u6613\u3044\uff0eB\u306fbase\u3067\u81ea\u660e\u3060\u304c\uff0cn\u306f\u5bfe\u8c61\u6570\uff0cK\u306f\u56fa\u5b9a\u306e\u9664\u6570\u306e\u30a4\u30e1\u30fc\u30b8\u304c\u3042\u308a\uff0cK\u3092\uff4e\u3068\u307f\u306a\u3059\u3053\u3068\u81ea\u4f53\u306b\u62b5\u6297\u304c\u3042\u308b\uff0eK\u3092\u0398\u3067\u7f6e\u304d\u63db\u3048\u3066\u307f\u3088\u3046\uff0e\u5c0f\u6587\u5b57\u306e\u03b8\u306f\u89d2\u5ea6\u3068\u3057\u3066\u666e\u904d\u7684\u306b\u4f7f\u308f\u308c\u3066\u3044\u308b\u304c\uff0c\u5927\u6587\u5b57\u306e\u0398\u306f\u3042\u307e\u308a\u4f7f\u308f\u308c\u3066\u3044\u306a\u3044\uff0e\u3053\u306e\u6587\u5b57\u3092\u9078\u3093\u3060\u7406\u7531\u306f\u5272\u308a\u7b97\u8a18\u53f7\u00f7\u306b\u5c11\u3057\u4f3c\u3066\u3044\u306a\u3044\u3053\u3068\u3082\u306a\u3044\u3068\u3044\u3046\u7406\u7531\u3060\uff0e\u039e\u304c111\u309290\u5ea6\u56de\u8ee2\u3055\u305b\u305f\u3082\u306e\u3068\u4f3c\u3066\u3044\u308b\u3068\u3044\u3046\u306e\u3068\u4f3c\u305f\u3088\u3046\u306a\u7406\u7531\u3060\uff0e<\/p>\n

\u305d\u3046\u306a\u308b\u3068\uff4e\u306e\u65b9\u306b\u3082\u30ae\u30ea\u30b7\u30e3\u6587\u5b57\u3092\u5272\u308a\u5f53\u3066\u305f\u65b9\u304c\u3088\u3055\u305d\u3046\u306a\u611f\u3058\u306b\u306a\u3063\u3066\u304f\u308b\uff0e\u3069\u3046\u305b\u306a\u3089\uff0cB\u3092\u03b2\u3068\u3057\uff0c\uff4e\u3092\u03b1\u3068\u3057\u3066\u307f\u3066\u306f\u3069\u3046\u3060\u308d\u3046\uff1f\u03b1\u3068\u03b2\u306f\u540c\u683c\u306a\u306e\u3067\u4e92\u3044\u306b\u5165\u308c\u66ff\u3048\u53ef\u80fd\u3068\u3044\u3046\u30a4\u30e1\u30fc\u30b8\u306b\u306a\u308b\uff0e\u3079\u304d\u5270\u4f59\u3068\u9006\u6570\u306e\u5faa\u74b0\u5c0f\u6570\u3092\u9023\u901a\u3055\u305b\u308b\u3068\u3044\u3046\u306e\u304c\u3053\u306e\u691c\u5b9a\u306e\u6700\u5927\u306e\u76ee\u7684\u3067\u3042\u308a\uff0c\u305d\u308c\u306b\u305d\u3046\u3068\u3059\u308c\u3070\u3053\u306e\u8fba\u308a\u3092\u660e\u78ba\u306b\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\uff0e\u03b1\/\u03b2\u3067\u306f\u306a\u304f\uff0cA\/B\u3068\u3044\u3046\u306e\u3067\u3082\u305d\u308c\u307b\u3069\u60aa\u304f\u306f\u306a\u3044\u3088\u3046\u306a\u6c17\u306f\u3059\u308b\uff0e\u305d\u3046\u306a\u308b\u3068\uff0c\u6307\u6570\u306ee\u3082\u30ae\u30ea\u30b7\u30e3\u6587\u5b57\u3067\u03b5\u3067\u306f\u306a\u3044\u3060\u308d\u3046\u304b\uff1fQ\u3068R\u306f\u82f1\u5b57\u3067\u6b8b\u3063\u3066\u3057\u307e\u3046\u304c\uff0c\u4ed5\u65b9\u306a\u3044\u3060\u308d\u3046\uff0e\u4eca\u5f8c\u306f\u3053\u306e\u8a18\u6cd5\u306b\u5f93\u3063\u3066\u8a18\u8ff0\u3059\u308b\u3053\u3068\u306b\u3059\u308b\uff0e<\/p>\n

\u03b5\u306b\u306f\u56fa\u5b9a\u306e\u30a4\u30e1\u30fc\u30b8\u304c\u3042\u308b\u306e\u3067\u4f7f\u3044\u3065\u3089\u3044\uff0e\u03b1\uff0c\u03b2\u306e\u6b21\u306e\u6587\u5b57\u03b3\u3092\u5272\u308a\u5f53\u3066\u308b\u3053\u3068\u306b\u3057\u3088\u3046\uff0e\u03b3\u306fstripe\u306b\u95a2\u4fc2\u3059\u308b\uff0e\u7e26\u6570\u5217\u306f\u307e\u3060\u3042\u307e\u308a\u6df1\u304f\u8abf\u3079\u3089\u308c\u3066\u3044\u306a\u3044\u306e\u3067\uff0c\u3053\u308c\u304b\u3089\u767a\u5c55\u3059\u308b\u9818\u57df\u3068\u8003\u3048\u3089\u308c\u308b\u306e\u3067\uff0c\u03b1, \u03b2\u3068\u540c\u683c\u306e\u6587\u5b57\u3092\u5272\u308a\u5f53\u3066\u3066\u304a\u304f\u306e\u306f\u9069\u5f53\u3060\u3068\u601d\u3046\uff0e<\/p>\n

\uff12\u3064\u554f\u984c\u304c\u3042\u308b\uff0e\uff081\uff09\u03b1=21, \u03b2=10\u3068\u3059\u308b\u3068U=47619, \u03b1U=999999\u30676\u6841\u306a\u306e\u3067@=6, \u307e\u305f\uff0c\u03b1\u3068\u03b2\u3092\u5165\u308c\u66ff\u3048\u3066\u03b1=10\u3068\u3057\uff0c\u0398=21\u3068\u3059\u308b\u3068\uff0c#=6, cycle={10,16,13,4,19,1}\u3068\u306a\u3063\u3066\uff0c\u4e0a\u306e\u8a18\u8ff0\u3068\u5408\u3063\u3066\u3044\u308b\u304c\uff0c\u03c8\u306e\u5024\u304c\u4e0d\u5b9a\u306b\u306a\u3063\u3066\u3044\u308b\uff0e\uff082\uff09U=47619*x and r=x, then the equation holds for any x \u3068\u3044\u3046\u554f\u984c\uff0e<\/p>\n

\u3053\u3053\u3067Get \u03c8\u3092\u5b9f\u884c\u3059\u308b\u3068\uff0c\u0398\u306f11\u306b\u4ee3\u308f\u308a\uff0c\u03c8=2\u304c\u8868\u793a\u3055\u308c\u308b\uff0e\u3053\u308c\u306f\u3069\u3061\u3089\u304b\u304c\u9593\u9055\u3063\u3066\u3044\u308b\u304b\u306a\u3044\u3057\uff0c\u7570\u306a\u308b\u5b9a\u7fa9\u306b\u3088\u3063\u3066\u3044\u308b\u3053\u3068\u306b\u306a\u308b\uff0e\u03c8\u95a2\u6570\uff08u-length function\uff09\u306e\u5b9a\u7fa9\u306b\u623b\u3063\u3066\u307f\u3088\u3046\uff0e<\/p>\n

Given mutually prime numbers n and b, there exist nonnegative integer x<n and positive integers y and z such that z=x*b^y \\n…x, that reads n divides x*b^y, the quotient z, and the remainder x, in other words, n*z+x=x*b^y. A set of {x,y,z} exists infinitely. u-length function y(b,n) is defined as the minimum such number y, as well recursion unit U(b,n) as the minimum such number z. <\/p>\n

\u4eca\u306e\u4e8b\u4f8b\u3067\u306f\uff0cn=21, b=10, z=47619, y=6 \u306e\u306f\u305a\u3060\u304c\uff0c\u5408\u3063\u3066\u3044\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3057\u3088\u3046\uff0e 21\uff6547619+x=10^6\uff65x \u2192 (10^6-1)x=999999\\x=21\uff6547619=999999 \u2234 x=1 \u78ba\u304b\u306b\u6570\u5024\u7684\u306b\u306f\u5408\u3063\u3066\u3044\u308b\u3088\u3046\u3060\uff0e\u03c8(b,n)\u306e\u5024\u306f\u305d\u306e\u3088\u3046\u306a\u95a2\u4fc2\u5f0f\u3092\u6e80\u8db3\u3059\u308b\u6700\u5c0f\u306e\uff59\u3068\u3055\u308c\u3066\u3044\u308b\u306e\u3060\u304b\u3089\uff0c\u3053\u3053\u3067\u306f\u03c8\u5024\u306f\u78ba\u5b9a\u3057\u3066\u3044\u308b\uff0e\u73fe\u884c\u30c4\u30fc\u30eb\u3067\u03c8\u5024\u3092\u3069\u306e\u3088\u3046\u306b\u6c7a\u5b9a\u3057\u3066\u3044\u308b\u304b\u3092\u898b\u3066\u307f\u3088\u3046\uff0e\u21d2PsiFunction\u3067\u306f\uff0c\u03c6(\u03b1)\u306e\u7d04\u6570\u304b\u3089\u03c8\u3092\u5272\u308a\u51fa\u3057\u3066\u3044\u308b\uff0e\u4eca\u03c6(\u03b1)=4\u306a\u306e\u3067\uff0c\u7d04\u6570\u5217\u306f{1,2,4}<\/p>\n

10^1%21=10, 10^2%21=10, 16, 10^4%21=4\u3067R=1\u304c\u51fa\u3066\u3053\u306a\u3044\uff0e\u306a\u308b\u307b\u3069\uff0c\u7406\u7531\u306f\u308f\u304b\u3063\u305f\uff0e\u03c8\u304c\u03c6\u306e\u7d04\u6570\u3067\u3042\u308b\u3068\u3044\u3046\u306e\u306f\u6b63\u3057\u3044\u304c\uff0c\u03c8\uff1d\u03c6\u306e\u5834\u5408\u304c\u3042\u308b\u3053\u3068\u3092\u898b\u843d\u3068\u3057\u3066\u3044\u308b\uff0e\u3053\u308c\u3092\u5165\u308c\u308c\u3070\u591a\u5206\u89e3\u3051\u308b\u306f\u305a\u3060\uff0e\u3044\u3084\uff0c\u9593\u9055\u3044\u3060\uff0e\u03c6\uff1d\uff14\u306f\u8a08\u7b97\u306b\u306f\u5165\u3063\u3066\u3044\u308b\uff0e\u03c8\u304c\u03c6\u306e\u7d04\u6570\u3067\u3042\u308b\u3068\u3044\u3046\u63a8\u8ad6\u304c\u9593\u9055\u3063\u3066\u3044\u308b\u306e\u3067\u306f\u306a\u3044\u3060\u308d\u3046\u304b\uff1f\u3044\u3084\uff0c\u3053\u308c\u306f\u5b9a\u7406\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u3063\u3066\u3044\u308b\uff0e<\/p>\n

P1(T):For any natural number n>2 on b-base decimal system, the value of u-length function y(b,n)>0 always divides the value of Euler’s totient function f(n), i.e., gcd(f(n),y(b,n)) = y(b,n). If n is a prime, then y(b,n) divides n-1.\n<\/p>\n

\u3069\u3046\u3082\u3053\u308c\u304c\u9593\u9055\u3044\u306e\u5143\u3067\u306f\u306a\u3044\u3060\u308d\u3046\u304b\uff1fWolfram MathWorld\u306eMultiplicable Order\u306e\u9805\u76ee\u306b\u3088\u308b\u3068\uff0c10^6\u22611 mod 7\u306a\u306e\u3067\uff0cord_7(10)=6\u3068\u306a\u3063\u3066\u3044\u308b\uff0e\u03c6(10)=4\u306a\u306e\u3067\uff0c\u03c8=6\u306f\u03c6=4\u3092\u5272\u308a\u5207\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\uff0e\u78ba\u304b\u306b\u73fe\u884c\u30d7\u30ed\u30b0\u30e9\u30e0\u3067\u306f\u3053\u306e\u3088\u3046\u306a\u5834\u5408\u306b\u306f\u300c\u4e92\u3044\u306b\u7d20\u3067PSI\u691c\u51fa\u4e0d\u80fd\u300d\u3068\u3044\u3046\u30e1\u30c3\u30bb\u30fc\u30b8\u3092\u51fa\u3057\u3066\u3044\u308b\uff0e<\/p>\n

https:\/\/mathworld.wolfram.com\/MultiplicativeOrder.html<\/a><\/p>\n

\u5fdc\u6025\u7684\u306b\u03b1\u306e\u3059\u3079\u3066\u306e\u3079\u304d\u3092\u30c6\u30b9\u30c8\u3059\u308b\u3088\u3046\u306b\u4fee\u6b63\u3057\u3066\u52d5\u4f5c\u3059\u308b\u3088\u3046\u306b\u306a\u3063\u305f\uff0e\u3053\u306e\u8ad6\u7406\u306f\u3082\u3057\uff0ccycle\u6570\u5217\u304c\u624b\u5143\u306b\u3042\u308c\u3070\uff0c\u3082\u3063\u3068\u9ad8\u901f\u5316\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u4e00\u884c\u3060\u3051\u3092\u51fa\u529b\u3059\u308b\u624b\u7acb\u3066\u306f\u3042\u308b\u3060\u308d\u3046\u304b\uff1f\u21d2\u5468\u671f\u6570\u5217\u306fDispResidueCycle\u3067\u8868\u793a\u3057\u3066\u3044\u308b\uff0e\u3053\u306e\u95a2\u6570\u306fResidueFuncPro\u304b\u3089\u547c\u3073\u51fa\u3055\u308c\u3066\u3044\u308b\u304c\uff0c\u3053\u306e\u6570\u5217\u3092\u5f97\u308b\u305f\u3081\u306b\u306fPowerResidueFunc\u3092\u5b9f\u65bd\u3059\u308b\u3053\u3068\u304c\u5fc5\u9808\u3060\uff0ePsiFunction\u306f\u5270\u4f59\u6f14\u7b97\u3068\u306f\u72ec\u7acb\u306b\u5b9f\u884c\u3067\u304d\u306a\u304f\u3066\u306f\u306a\u3089\u306a\u3044\u304b\u3089\uff0c\u72ec\u81ea\u306bcycle\u3092\u53d6\u5f97\u3067\u304d\u308b\u3088\u3046\u306b\u3059\u308b\u3079\u304d\u3060\u308d\u3046\uff0e\u3053\u308c\u306fBuildMatrix\u3067\u3084\u3063\u3066\u3044\u308b\u3053\u3068\u306e\u4e00\u90e8\u3092\u5207\u308a\u51fa\u3059\u3053\u3068\u306b\u5f53\u305f\u308b\uff0e\u21d2GetResiduCycle\u3068\u3044\u3046\u95a2\u6570\u3092\u4f5c\u3063\u305f\uff0e\u3053\u308c\u3067\u03c8\u5024\u306e\u8a08\u7b97\u306b\u306fFactoring\u304c\u4e0d\u7528\u306b\u306a\u308a\uff0c\u7121\u8336\u82e6\u8336\u9ad8\u901f\u5316\u3055\u308c\u305f\uff0e<\/p>\n

\u3084\u306f\u308a\uff0c\u03c8\u304c\u03c6\u3092\u5272\u308a\u5207\u308b\u3068\u3044\u3046\u306e\u306f\u5b8c\u5168\u306a\u8aa4\u308a\u3067\u3042\u308b\u3088\u3046\u306b\u601d\u308f\u308c\u308b\uff0e\u03b1=29\u3067\u0398=59\u306e\u3068\u304d\uff0c\u03c6=28\u3067\u03c8\u306f29\u306b\u306a\u308b\uff0e\u5270\u4f59\u6570\u5217\u306f\u4e0b\u8a18\u306e\u3088\u3046\u306a\u3082\u306e\u306b\u306a\u3063\u3066\u3044\u308b\uff0e<\/p>\n

{29,15,22,48,35,12,53,3,28,45,7,26,46,36,41,9,
25,17,21,19,20,49,5,27,16,51,4,57,1,29,}<\/p>\n

\u03b1\u306f29\u3067\u7d20\u6570\u3060\u304b\u3089\uff0c\u03c6\u306f\u5f53\u713628\u306b\u306a\u308b\uff0e\u3053\u306e\u3068\u304d\uff0c\u03c8\u5024\u306f29\u3067\u03c6\u3088\u308a\u3082\u5927\u304d\u3044\u6570\u306b\u306a\u3063\u3066\u3044\u308b\u304b\u3089\uff0c\u5f53\u7136\u03c6\u3092\u5272\u308a\u5207\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\uff0e\u0398\u304c\u03b1\u3088\u308a\u3082\u5c0f\u3055\u3044\u3068\u304d\u306b\u306f\u3082\u3057\u304b\u3059\u308b\u3068\u03c8\u304c\u03c6\u3092\u5272\u308a\u5207\u308b\u3068\u3044\u3046\u3053\u3068\u304c\u6210\u7acb\u3057\u3066\u3044\u308b\u306e\u304b\u3082\u3057\u308c\u306a\u3044\u304c\u2026\u3044\u305a\u308c\u306b\u305b\u3088\uff0c\u4f55\u3089\u304b\u306e\u6761\u4ef6\u304c\u306a\u3051\u308c\u3070\u6210\u7acb\u3057\u306a\u3044\u3082\u306e\u3068\u601d\u308f\u308c\u308b\uff0e\u21d2\u975e\u5e38\u306b\u91cd\u8981\u306a\u3053\u3068\u3092\u767a\u898b\u3057\u305f\uff0e\u3053\u308c\u306f\u4ee5\u524d\u306b\u3069\u3053\u304b\u306b\u66f8\u3044\u305f\u3053\u3068\u304c\u3042\u308b\u3088\u3046\u306a\u6c17\u304c\u3059\u308b\u304c\uff0c\u03b1\u3068U\u306f\u3042\u308b\u57fa\u6570B\u306e\u9032\u6570\u30b7\u30b9\u30c6\u30e0\u4e0a\u3067\u300c\u9006\u5143\u300d\u3067\u3042\u308b\u3068\u8a00\u3048\u308b\uff0e\u4e0b\u56f3\u3092\u898b\u308b\u3068\uff0c\u3053\u306e\u3053\u3068\u304c\u7591\u554f\u306e\u4f59\u5730\u306a\u304f\u78ba\u8a8d\u3067\u304d\u308b\uff0e<\/p>\n

\"image\"<\/a><\/p>\n

\u3044\u3084\uff0c\u9006\u5143\u3068\u8a00\u3046\u304b\u3089\u306b\u306f\uff0ca \u2715 a^-1\uff1d\uff11\u3068\u306a\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u306a\u304f\u3066\u306f\u306a\u3089\u306a\u3044\uff0e\u78ba\u304b\u306b\u305d\u3093\u306a\u7c21\u5358\u306a\u3082\u306e\u3067\u306f\u306a\u3044\uff0e123 x 813 = 99999\u3060\uff0e\u3053\u308c\u3092\u898b\u3066\u8a00\u3048\u308b\u3053\u3068\u306f\uff0c99999\u3092\u5358\u5143\u3068\u307f\u306a\u3059\u3053\u3068\u304c\u3067\u304d\u308c\u3070\uff0c\u78ba\u304b\u306b\u3053\u306e\uff12\u3064\u306e\u4e0b\u56f3\u306f\u4e92\u3044\u306e\u9006\u6570\u3067\u3042\u308b\u3068\u8a00\u3048\u308b\u3060\u308d\u3046\uff0e\u4eee\u306b999\u2026999\u306e\u3088\u3046\u306a\u5f62\u306e\u3059\u3079\u3066\u306e\u6570\u3092\u5358\u4f4d\u5143\u3068\u307f\u306a\u3059\u3068\u3057\u3066\u3082\uff0c999\u2026999\u306e\u7d04\u6570\u3068\u306a\u3089\u306a\u3044\u6570\u306f\u3044\u304f\u3089\u3067\u3082\u3042\u308b\u306f\u305a\u3060\uff0eWolffram\u306e\u30da\u30fc\u30b8\u306b\u306f\u4e0b\u306e\u3088\u3046\u306a\u8868\u304c\u63b2\u8f09\u3055\u308c\u3066\u3044\u308b\uff0e\u3053\u306e\u7a0b\u5ea6\u306e\u3082\u306e\u306f\u51fa\u529b\u3067\u304d\u308b\u3088\u3046\u306b\u3057\u3066\u304a\u304d\u305f\u3044\uff0e<\/p>\n

Multiplicative Order<\/h3>\n

\"image\"<\/a><\/p>\n

\u25b2Get \u03c8\u306f\u307b\u3068\u3093\u3069\u4e0d\u7528\u306b\u306a\u3063\u305f\uff0e<\/p>\n

\u25b2<\/font>\u9053\u5177\u7bb1\u304b\u3089\u8907\u6570\u306e\u753b\u9762\u3092\u958b\u3051\u308b\u3088\u3046\u306b\u3059\u308b\uff0e\u306a\u3044\u3057\uff0c\u51fa\u529b\u753b\u9762\u3092\u9053\u5177\u7bb1\u306b\u79fb\u3059\uff0e\u21d2\u5b8c\u5168\u306b2\u3064\u306e\uff08\u7b49\u30b5\u30a4\u30ba\u306e\uff09\u30a6\u30a3\u30f3\u30c9\u30a6\u306b\u5206\u5272\u3057\u305f\uff0e<\/p>\n

\"image\"<\/a><\/p>\n

\u3053\u308c\u3057\u304b\u306a\u3044\uff0e\u30bf\u30d6\u306b\u3057\u3066\u3082\u3088\u3044\u306e\u3060\u304c\uff0c\u305d\u3046\u3059\u308b\u3068\u51fa\u529b\u753b\u9762\u3068\u30d1\u30cd\u30eb\u3092\u540c\u6642\u306b\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u3044\uff0e\u51fa\u529b\u753b\u9762\u306f\u4e0d\u7528\u306a\u3068\u304d\u306b\u306f\u9589\u3058\u3066\u30a2\u30a4\u30b3\u30f3\u5316\u3057\u3066\u304a\u304f\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u9053\u5177\u7bb1\u3092\u9589\u3058\u308b\u3068\u30a2\u30d7\u30ea\u7d42\u4e86\u3059\u308b\uff0e<\/p>\n

\u25b2<\/font>\u539f\u59cb\u6839\u30de\u30fc\u30af\u304c\u9593\u9055\u3063\u3066\u3044\u308b\u3088\u3046\u3060\uff0e\u03b1=123488\u3067\u0398\uff1d5\u306e\u3068\u304d\uff0c\u03b1\u306b\u30de\u30fc\u30af\u304c\u4ed8\u3044\u3066\u3044\u308b\u304c\uff0ccycle\u306f0#0\u30673.\u3068\u8868\u793a\u3055\u308c\u3066\u3044\u308b\u3060\u3051\u3060\uff0e\u305d\u3082\u305d\u3082cycle\u306e\u8868\u793a\u304c\u304a\u304b\u3057\u304f\u306a\u3063\u3066\u3044\u308b\uff0e\u3069\u3053\u304b\u58ca\u3057\u3066\u3057\u307e\u3063\u305f\u306e\u3060\u308d\u3046\u304b\uff1fcycle\u3092\u8868\u793a\u3057\u3066\u3044\u308b\u306e\u306fDispResidueCycle\u3060\uff0e\u3053\u306e\u95a2\u6570\u306b\u6e21\u3055\u308c\u308bdrop\u3068period\u304c\u9593\u9055\u3063\u3066\u3044\u308b\u306e\u3060\u308d\u3046\uff0e\u304a\u304b\u3057\u3044\uff0e\u3053\u3093\u3069\u306f\u6b63\u3057\u304f\u8868\u793a\u3055\u308c\u3066\u3044\u308b\uff0e\u958b\u59cb\u6642\u70b9\u306e\u03b1=123456\uff0c\u0398=7\u306b\u623b\u3063\u3066\u3084\u308a\u76f4\u3057\u3057\u3066\u307f\u3088\u3046\uff0e\u9014\u4e2d\u3067\u5de8\u5927\u306a\u30ec\u30d4\u30e5\u30cb\u30c3\u30c8\u6570\u304c\u51fa\u73fe\u3057\u3066\u3044\u308b\u306e\u304c\u95a2\u4fc2\u3057\u3066\u3044\u308b\u306e\u304b\u3082\u3057\u308c\u306a\u3044\uff0e6498\u6841\u3082\u3042\u308b\u6570\u3092\u30c0\u30f3\u30d7\u3059\u308b\u3068\u3044\u3046\u306e\u304c\u7121\u8336\u3060\uff0eMakeRecursionUnit\u3067\u3082\u5de8\u5927\u6570\u3092\u30c0\u30f3\u30d7\u3057\u3066\u3044\u308b\uff0e<\/p>\n

\u73fe\u5728MakeRecursionUnit\u3067\u306fMAXTEXTLENGTH=32767\u3092\u4e0a\u9650\u3068\u3057\u3066\u3044\u308b\u304c\uff0c\u3055\u3059\u304c\u306b\u5927\u304d\u904e\u304e\u308b\u306e\u3067\u306f\u306a\u3044\u304b\uff1fMaxOutput=10000\u306b\u843d\u3068\u3057\u305f\uff0e\u3060\u3044\u3076\u697d\u306b\u306a\u3063\u305f\uff0e<\/p>\n

\u25b2<\/font>\u0398=8\u3067\u03b1\u3092\u5909\u3048\u3066\u3044\u305f\u3089\uff0c\u03b1202\u306e\u8fba\u308a\u3067\u30cf\u30f3\u30b0\u3057\u3066\u3057\u307e\u3063\u305f\uff0ekinai\u306f\uff13\u3064\u8d70\u3063\u3066\u3044\u308b\uff0eVS19\u3082\uff12\u3064\u8d70\u3063\u3066\u3044\u308b\uff0e\u21d2\u5236\u5fa1\u304c\u623b\u3063\u3066\u304d\u305f\uff0e\u30a4\u30d9\u30f3\u30c8\u304c\u6ede\u7559\u3057\u3066\u3053\u306a\u3059\u306e\u306b\u6642\u9593\u304c\u639b\u304b\u3063\u3066\u3044\u305f\u305f\u3081\u3060\uff0e<\/p>\n

\u25b2cycle\u306f\u91cd\u8907\u3057\u306a\u3044\u6587\u5b57\u5217\u3067\u3088\u3044\uff0e\uff08\u672b\u5c3e\u306e\uff11\u6587\u5b57\u306f\u4f59\u5206\uff09\u6841\u6570\uff03\u5206\u3060\u3051\u51fa\u305b\u3070\u3088\u3044\uff0e<\/p>\n

\u25b2<\/font>cycle\u306edrop\u30681\/\u03b1\u306efixed\u306b\u8a18\u53f7\u3092\u4e0e\u3048\u308b\uff0e\u21d2\u4f7f\u3048\u308b\u4f59\u767d\u304c\u306a\u3044\u306e\u3067\uff0c\u73fe\u72b6\u306e\u307e\u307e\u3068\u3059\u308b\uff0e\u7121\u540d\u306e\u5024\u3092\u53c2\u7167\u3059\u308b\u3068\u304d\u306b\u306f [3#12]\uff0c[0@23]\u306a\u3069\u306e\u3088\u3046\u306b\u8868\u8a18\u3057\u3066\u533a\u9593\u306b\u95a2\u4fc2\u3059\u308b\u5024\u3067\u3042\u308b\u3053\u3068\u3092\u6697\u793a\u3059\u308c\u3070\u3088\u3044\uff0e<\/p>\n

<\/font><\/p>\n","protected":false},"excerpt":{"rendered":"

Get\u03c8\u95a2\u6570\u306e\u4ed5\u69d8\u3092\u518d\u8003\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\uff0e\u03c8\u6570\u306f\uff4e\u3068K\u306b\u3088\u3063\u3066\u6c7a\u307e\u308b\u304c\uff0c\u03c8\u6570\u304c\u6c7a\u5b9a\u3067\u304d\u306a\u3044\u5834\u5408\u3082\u3042\u308b\uff0e\u03c8\u6570\u304c\u5f97\u3089\u308c\u308b\u6761\u4ef6\u306fN\u306e\u3079\u304d\u5270\u4f59\u6570\u5217\u306e\u4e2d\uff08\u7d42\u7aef\uff09\u306b\uff11\u304c\u73fe\u308c\u308b\u3053\u3068\u3060\u304c\uff0c\u5270\u4f59\u6570\u5217\u306b\uff11\u304c\u5165\u3089\u306a\u3044\u5834\u5408\u306f\u3044\u304f\u3089\u3067\u3082\u3042\u308b\uff0e\u3053\u306e\u3088 … <\/p>\n

“ψ\u304cφ\u3092\u5272\u308a\u5207\u308b\u3068\u3044\u3046\u306e\u306f\u5b9a\u7406\u3067\u306f\u306a\u3044” \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"_links":{"self":[{"href":"https:\/\/zelkova-tree.net\/WordPress\/wp-json\/wp\/v2\/posts\/14716"}],"collection":[{"href":"https:\/\/zelkova-tree.net\/WordPress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/zelkova-tree.net\/WordPress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/zelkova-tree.net\/WordPress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/zelkova-tree.net\/WordPress\/wp-json\/wp\/v2\/comments?post=14716"}],"version-history":[{"count":16,"href":"https:\/\/zelkova-tree.net\/WordPress\/wp-json\/wp\/v2\/posts\/14716\/revisions"}],"predecessor-version":[{"id":14732,"href":"https:\/\/zelkova-tree.net\/WordPress\/wp-json\/wp\/v2\/posts\/14716\/revisions\/14732"}],"wp:attachment":[{"href":"https:\/\/zelkova-tree.net\/WordPress\/wp-json\/wp\/v2\/media?parent=14716"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zelkova-tree.net\/WordPress\/wp-json\/wp\/v2\/categories?post=14716"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zelkova-tree.net\/WordPress\/wp-json\/wp\/v2\/tags?post=14716"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}