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Home » \(5^2 + b^2 = 13^2\) - Appfinity Technologies

\(5^2 + b^2 = 13^2\) - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Here, $ a = 12 $, $ b = 18 $, so $ \gcd(12, 18) = 6 $.

📌 \gcd(2^{12} - 1, 2^{18} - 1) = 2^6 - 1 = 64 - 1 = 63

📌 Therefore, the greatest common divisor is $ \boxed{63} $.

📌 Question: What is the largest integer that must divide the product of any four consecutive positive integers?

📌 Solution: Let the four consecutive integers be $ n, n+1, n+2, n+3 $.

📌 Among any four consecutive integers:

📌 There are at least two even numbers, and one of them is divisible by 4 → total factor of $ 2^3 = 8 $

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