prove that (3)*5^(2n+1)+2^(3n+1) is divisible by 17

= 3 * 5 * 5^(2n) + 2 * (2^3)^n mod 17
= 15 * 25^n + 2 * 8^n mod 17
= 1 5 * 8^n + 2 * 8^n mod 17 as 25 = 8 mod 17
= 17 * 8^n

hence divisible by 17