# Divisible

• Feb 9th 2008, 06:38 AM
Divisible
Prove that $7|5^{2n}+(3)(2^{5n-2})$

I tried to use induction on this one. The statement is true for n = 1, assume k is true.

I have $5^{2k+2}+3(2^{5k+3})$

Then $5^{2k}(25)+3(2^{5k-2})(32) \equiv 5^{2k}(4)+3(2^{5k-2})(4) \equiv 0 \ (mod \ 7)$

This right?
• Feb 10th 2008, 12:16 AM
CaptainBlack
Quote:

Prove that $7|5^{2n}+(3)(2^{5n-2})$
I have $5^{2k+2}+3(2^{5k+3})$
Then $5^{2k}(25)+3(2^{5k-2})(32) \equiv 5^{2k}(4)+3(2^{5k-2})(4) \equiv 0 \ (mod \ 7)$