Your idea is sound. Here is a hint note that
Not that is even so 2 divides it and
by fermat's little theorem
Use these two facts to show that 14 divides
and so the euclidean algorithm terminates.
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.