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.
平方余数
记r是(a?1)n + (a+1)n被a2除所得的余数。
例如，如果a = 7而n = 3，则r = 42：63 + 83 = 728 ≡ 42 mod 49。随着n的变化，r也会随之变化，但是对a = 7，可以得出rmax = 42。
对于3 ≤ a ≤ 1000，求∑rmax。