PUMaC 2012 · 数论（B 组） · 第 7 题
PUMaC 2012 — Number Theory (Division B) — Problem 7
题目详情
- [ 7 ] Find the sum of all possible sums a + b where a and b are nonnegative integers such that a b 4 + 2 + 5 is a perfect square. p n − 1
解析
- [ 7 ] Find the sum of all possible sums a + b where a and b are nonnegative integers such that a b 4 + 2 + 5 is a perfect square. Solution: This question is based on quadratic residues. If a > 1 and b > 2 then the resulting number is 5 (mod 8), hence not a perfect square. Then we check other cases 1 by 1: a