Math Help - Proving gcd(5^98 + 3, 5^99 +1 ) = 14

1. Proving gcd(5^98 + 3, 5^99 +1 ) = 14

Hello,

this is my first time using a forum for mathematics.

I have come across a question that I am unable to solve.

Prove that gcd(5^98 + 3, 5^99 +1) = 14

I've been thinking about it and I believe that using the euclidean algorithm would work, but I am unsure on how to approach it.

2. Your idea is sound. Here is a hint note that

Not that $5^{98}+3$ is even so 2 divides it and

by fermat's little theorem $5^{6} \equiv 1 \test{mod}(7)$

Use these two facts to show that 14 divides $5^{98}+3$

and so the euclidean algorithm terminates.