Question 29
Prove that, for positive integers $n$ and $m$,
$$
\operatorname{gcd}\left(2^{m}-1,2^{n}-1\right)=2^{\operatorname{gcd}(m, n)}-1
$$
$$
\operatorname{gcd}\left(2^{m}-1,2^{n}-1\right)=2^{\operatorname{gcd}(m, n)}-1
$$
MathNet 2026 — Part 10 Question 29
Math Olympiad Vault · MathNet 2026 — Part 10