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pictures of a cartoon monkey - Professionaloutdoormedia

📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 Total probability:

📌 \cdot \frac{32}{6561} = \frac{640}{6561}

📌 Thus, the probability is:

📌 \boxed{\frac{640}{6561}}

📌 $$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.

📌 We compute $ \gcd(24, 36) $. Using the Euclidean algorithm:

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