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Home » Shocking Discovery: Tactile Fremitus Could Revolutionize Touch-Based Diagnostics! - Red Crowns

Shocking Discovery: Tactile Fremitus Could Revolutionize Touch-Based Diagnostics! - Red Crowns

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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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.

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

📌 \gcd(36, 24) = \gcd(24, 12) = \gcd(12, 0) = 12.

📌 \gcd(5^{24} - 1, 5^{36} - 1) = 5^{12} - 1.

📌 We now compute $ 5^{12} - 1 $:

📌 5^2 = 25, \quad 5^4 = (25)^2 = 625, \quad 5^8 = 625^2 = 390625,

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