continued fraction 썸네일형 리스트형 Problem 66 - Investigate the Diophantine equation x2 − Dy2 = 1. 링크 Consider quadratic Diophantine equations of the form: x2 – Dy2 = 1 For example, when D=13, the minimal solution in x is 6492 – 131802 = 1. It can be assumed that there are no solutions in positive integers when D is square. By finding minimal solutions in x for D = {2, 3, 5, 6, 7}, we obtain the following: 32 – 222 = 1 22 – 312 = 1 92 – 542 = 1 52 – 622 = 1 82 – 732 = 1 Hence, by considering .. 더보기 Problem 64 - How many continued fractions for N ≤ 10000 have an odd period? 링크 All square roots are periodic when written as continued fractions and can be written in the form: N = a0 + 1 a1 + 1 a2 + 1 a3 + ... For example, let us consider 23: 23 = 4 + 23 — 4 = 4 + 1 = 4 + 1 1 23—4 1 + 23 – 3 7 If we continue we would get the following expansion: 23 = 4 + 1 1 + 1 3 + 1 1 + 1 8 + ... The process can be summarised as follows: a0 = 4, 1 23—4 = 23+4 7 = 1 + 23—3 7 a1 = 1, 7.. 더보기 이전 1 다음