PUMaC 2012 · 数论（B 组） · 第 5 题
PUMaC 2012 — Number Theory (Division B) — Problem 5
题目详情
- [ 5 ] How many ways can 2 be expressed as the sum of four (not necessarily distinct) positive squares? 2
解析
- b = 2. This becomes 4 + 9, and if a > 2 then (2 ) < 4 + 9 < (2 + 1) , and only when a = 2 we get a perfect square. Hence only solution in this case is a = b = 2. And so we get the solutions a = 1 , b = 4 and a = b = 2. Thus, our answer is 9 . Problem contributed by Chengyue Sun. p n − 1