Question

prove that 21 divides 4^(n+1)+5^(2n-1) whenever n is a positive integer.

Answer 1

by using mathematical induction

Answer 2

1. Prove the statement for n=1
2. Assume the statement is true for n and prove that this implies it's true for n+1 too.

Step one is straightforward. For step 2 you could take the difference of the expression for n+1 and n and check if it's divisible by 21.