Your Daily Epsilon of Math 2023

  1. 2023-01-01 整方程式の定数項は根の約数:Let p(y) be a polynomial with integer coefficients. p(0)=104729 x, x∈Z such that p(x) = x and 0<x<104729
  2. 2023-01-02 部分分数分解による無限級数の和:(lim{n→∞}1/(2n-1)(2n+1))^-1
  3. 2023-01-03 数学パズル:111/(1+1+1) + 222/(2+2+2) + …+ 999/(9+9+9)
  4. 2023-01-04 整係数方程式の有理数解 -x^4+16x^3-96x^2+256x-256=0
  5. 2023-01-05 ピタゴラスの定理:The area of the square ABCD is 20.25. Find EC. (Round)
  6. 2023-01-06 合成関数(三角関数)の微分:Find the value of the derivative of f(x)=sin(x^3+6x) at x=0
  7. 2023-01-07 直線で囲まれた矩形面積:What is the area bounded by y=3-4x/9, x=3 and the x and y axes?
  8. 2023-01-08 三角関数,逆三角関数:cot^2(π/6)+csc(5π/6)+3tan^2(π/6)+sec(11π/6)cot(7π/6)
  9. 2023-01-09 階乗:4!÷4+(4-4÷4)
  10. 2023-01-10 三角関数の積分:∫{0~4π}(20x^2 + 30sin~2(x))dx / (x^2cos^2(x) + cos^2(x)) (Round)
  11. 2023-01-11 階乗:(x!)^2/(x-1)!(x+1)! = 11/22
  12. 2023-01-12 方角・距離:Anirban runs to a tree 2 m north of his starting location, then runs to a spot 4 m south and 8 m west of his starting location. How far did he run?
  13. 2023-01-13 タイリング問題:How many ways are there of tiling a 2×6 space with 2×1 tiles?
  14. 2023-01-14 正七角形,二面体群,対称群:What is the order of the symmetry group of a regular heptagon.
  15. 2023-01-15 指数計算:225^1/200*225^3/200*225^5/200*…*225^19/200
  16. 2023-01-16 複素数の乗除算,極座標表示:(i-1)^8
  17. 2023-01-17 接線の傾き,合成関数の微分:Find the slope of the line tangent to the curve y=2^x at x=4.6 (Round)
  18. 2023-01-18 連立整方程式:For a, b, c, d, x positive integers : abcd = 8!, ab+a+b=524, bc+b+c=146, cd+c+d=104, a-c=x
  19. 2023-01-19 素因数分解:Find the second smallest prime factor of 1,000,027
  20. 2023-01-20 四面体数・三角数:What is the fourth tetrahedral number?
  21. 2023-01-21 直線の傾き:Find the slope of the line that passes through (-10, –21) and (-7, 42)
  22. 2023-01-22 1次方程式:(8-x)/(1-x) = 2/3
  23. 2023-01-23 交差図形の面積,定積分による求積:Four circles inscribed by a big circle. An uncovered area = 23. What is the area x of a crossing area?
  24. 2023-01-24 待ち行列,n次対称群(n次置換群):How many ways can Alfonso, Bianca, Catriona, and Domingo queue up?
  25.  2023-01-25 地図の縮尺:If two mountain peaks are 10 cm apart on a map with scale 4 cm to 10 km, how many kilometers separate the peaks?
  26. 2023-01-26 無限級数の和,区分求積法,置換積分,マクローリン展開:13e^(1-1/2+1/3-1/4+…)
  27. 2023-01-27 三角形の面積,三角形の相似:An equilateral triangle of area=9 is inscribed by an equilateral triangle. Find the area of the outer triangle.
  28. 2023-01-28 MMMMDCCLVI÷CXVI-XIII
  29. 2023-01-29 平面的最短距離,展開図:What is the shortest distance from A to B on the outside of the box?
  30. 2023-01-30 余弦定理・ヘロンの公式:In the diagram a square is placed on each side of a right triangle (5, 12, 13) . How much the area sandwiched  by the square 5 and square 13?
  31. 2023-01-31 二次方程式:Find the smaller root of x^2-103x+2232=0
  32. 2023-02-01 開被覆,開集合,閉包:For any set X ∈ [0, 1], let E(X) be the largest value such that for any open cover of X, the sum of its lengths ≧E(X). If Z={Q∩[0, 1]}, what is E([0, 1])-E(Z)?
  33. 2023-02-02 対数計算:1/log4(10) + 2/log5(10)
  34. 2023-02-03 置換積分法(合成関数の積分):π/∫{0→1}1/sqrt(x)sqrt(4-x) dx
  35. 2023-02-04 フィボナッチ数列,ピタゴラス数:Starting with x+1, every second Fibonacci number is the largest number in a Pythagorean triple.
  36. 2023-02-05 方べきの定理:The circumference/inscribed angle theorem
  37. 2023-02-06 整係数方程式の有理解,定数項の約数:Find the integer x that (x-3)^3+(x-2)^3+(x-1)^3=x^3
  38. 2023-02-07 因子木:All letters in this factor tree represent distinct digits. Primes are circled.
  39. 2023-02-08 三角形の面積:Find the triangular area from given value of sides of the squares.
  40. 2023-02-09 両替問題:How many ways can you make change for a twenty collar bill with one, five, and ten dollar bills.
  41. 2023-02-10 関数の最小値,導関数=0,合成関数の微分:Find the minimum value of sqrt(x^2+1+2/x+1/x^2) + sqrt(x^2-12x+85-14/x+1/x^2)
  42. 2023-02-11 素因数分解:Find the number of odd numbers that divide 3^12-1 but do not divide any of 3^11-1, 3^10-1, …, 3^1-1
  43. 2023-02-12 倍角・半角の公式,加法定理:tan(θ)=(sqrt(145) – 1)/12  Find tan(2θ)
  44. 2023-02-13 排他的論理和:10110B ⊕ 11011B
  45. 2023-02-14 複素数:(3-i)(2+i) + (3+i)(2-i)
  46. 2023-02-15 合同式,フェルマーの小定理,2項定理:15^113 mod 113
  47. 2023-02-16 複素数累乗根:Find the sum of the absolute value of the real parts of the roots of  z^3 – 512
  48. 2023-02-17 三角形の面積:area(⊿ABC)=136 The degrees of ∠ABC is optional and the ratio of the sides AB : BC is free, hence the length of AC is arbitrary. Then how on earth the assigned area can be determined?
  49. 2023-02-18 切頂4面体:How many edges does a truncated tetrahedron have?
  50. 2023-02-19 整数解:A and B are whole numbers such that A/3 + B/37 = 91/111  Find A+B
  51. 2023-02-20 合成関数(有理関数)の微分:Find the derivative of  f(x) = (x^2-10)/(2x+1) at x = 0
  52. 2023-02-21 完全平方数:What is the smallest integer n such that 4725/n is a perfect square?
  53. 2023-02-22 長方形の面積:Find the third area from given two areas and two sides
  54. 2023-02-23 交代数列の累和:–1 + 2 – 3 + 4 – 5 + 6 – … –45 + 46
  55. 2023-02-24 順列・組み合わせ:Four cards are drawn at random from a deck numbered 1 to 100. What is the inverse of the probability that the cards are drawn in increasing order?
  56. 2023-02-25 指数関数の極限公式,ロピタルの定理:lim{x→0}(5x/(e^0.2x – 1))
  57. 2023-02-26 二次方程式:x^2-(x-2)^2=100
  58. 2023-02-27 ウィルソンの定理:(16!)^2 mod 37
  59. 2023-02-28 1次方程式:(x + 7) / 5 = x / 4

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