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Home » Wait — is it possible that $ d(1)=1 $, $ d(2)=8 $, $ - Groen Casting

Wait — is it possible that $ d(1)=1 $, $ d(2)=8 $, $ - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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Here, $ a = 12 $, $ b = 18 $, so $ \gcd(12, 18) = 6 $.
Thus,
\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...
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...
There is exactly one multiple of 4 and another even, so $ 8 \mid $ pro...
There is at least one multiple of 3 → $ 3 \mid $ product

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