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$$Question: What is the greatest common divisor of $ 5^m - 1 $ and $ 5^n - 1 $, where $ m = 24 $ and $ n = 36 $?
Solution: The greatest common divisor of $ 5^m - 1 $ and $ 5^n - 1 $ for positive integers $ m $ and $ n $ is given by the identity:
\gcd(5^m - 1, 5^n - 1) = 5^{\gcd(m,n)} - 1.

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