# Problem 120: Square remainders
Let r be the remainder when (a−1)n + (a+1)n is divided by a2. For
example, if a = 7 and n = 3, then r = 42: 63 + 83 = 728 ≡ 42 mod 49. And
as n varies, so too will r, but for a = 7 it turns out that rmax = 42.
For 3 ≤ a ≤ 1000, find ∑ rmax.