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📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \Rightarrow 55^2 \equiv 6^2 = 36 \equiv 1 \pmod{7}

📌 Alternatively, $ 3025 \div 7 = 432 \text{ remainder } 1 $, so $ 3025 \equiv 1 \pmod{7} $.

📌 Therefore, the remainder is $ \boxed{1} $.

📌 Question: What is the greatest common divisor of $ 2^{12} - 1 $ and $ 2^{18} - 1 $?

📌 Solution: We use the identity:

📌 \gcd(2^a - 1, 2^b - 1) = 2^{\gcd(a,b)} - 1

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

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