# 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