Computing $\gcd$ of very large numbers with powers

Question

How to calculate $\gcd$ of $5^{2^{303} - 1} - 1$ and $5^{2^{309} - 1} - 1$?

I stumbled upon this interesting problem and tried elementary algebraic simplification and manipulation. But found no success.

Why would that be an interesting problem? – Henrik supports the community Mar 29 '18 at 10:53 — Henrik supports the community, Mar 29 '18 at 10:53
I think it's interesting because of its solution. – Max Freiburghaus Mar 29 '18 at 10:54 — Max Freiburghaus, Mar 29 '18 at 10:54

score 2 · Answer 1 · answered Mar 29 '18 at 10:51

2

Hint:

$$gcd(5^a - 1,5^b -1) = 5^{gcd(a,b)} -1$$

answered Mar 29 '18 at 10:51

kayush

1 Answers1