It is proved that 8 ^ 2n + 1 + 7 ^ (n + 2) is a multiple of 57

It is proved that 8 ^ 2n + 1 + 7 ^ (n + 2) is a multiple of 57

Mathematical induction
When n = 1, 8 ^ (2n + 1) + 7 ^ (n + 2) = 8 ^ 3 + 7 ^ 3 = 855 = 57 * 15 holds
Suppose n = k, that is, 8 ^ 2n + 1 + 7 ^ (n + 2) is a multiple of 57, then 8 ^ (2k + 1) + 7 ^ (K + 2) = 57M, M is a positive integer
When n = K + 1, 8 ^ [2 (K + 1) + 1] + 7 ^ (K + 1 + 2) = 8 ^ (2k + 1) + 7 ^ (K + 2) + 8 ^ 3 + 7 ^ 3 = 57M + 57 * 15 = 57 (M + 15)
The proposition holds