PUMaC 2010 · 数论（A 组） · 第 8 题
PUMaC 2010 — Number Theory (Division A) — Problem 8
题目详情
- A consecutive pythagorean triple is a pythagorean triple of the form a + ( a + 1) = b , a and b positive integers. Given that a , a + 1, and b form the third consecutive pythagorean triple, find a . 1
解析
- An awesome pythagorean triple is a pythagorean triple of the form a + ( a + 1) = b , a and b positive integers. Given that a , a + 1, and b form the third positive awesome pythagorean triple, find a . 2 2 2 2 Solution: The equation is 2 a + 2 a + 1 = b , which can be rearranged to (2 a + 1) − 2 b = − 1. √ √ n The solutions to that are given by the coefficients of (1 + 2)(3 + 2 2) , and one gets a values 0 (trivial and ignored), 3, 20, and 119, so 119 is the answer. 2