Let
be positive integers such that
and
Prove that if
and
have the same prime divisors, then
is a power of 2.
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Let $b, m, n$ be positive integers such that $b > 1$ and $m \neq n.$ Prove that if $b^m - 1$ and $b^n - 1$ have the same prime divisors, then $b + 1$ is a power of 2.
Školjka