Question 70
Let $a$, $b$ and $n$ be positive integers with $\text{GCD}(a, b) = 2009$. Prove that
$$
\text{GCD}(n^a - 1, n^b - 1) = n^{2009} - 1.
$$
$$
\text{GCD}(n^a - 1, n^b - 1) = n^{2009} - 1.
$$
MathNet 2009-part-01 — 175 problems (EN–VI) Question 70
Math Olympiad Vault · MathNet 2009-part-01 — 175 problems (EN–VI)