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📅 May 3, 2026 👤 scraface

May 03, 2026

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🔥 Popular Posts

Question: What is the largest integer that must divide the product of...
Solution: Let the four consecutive odd integers be $n, n+2, n+4, n+6$,...
P = n(n+2)(n+4)(n+6)
We seek the largest integer that divides $P$ for all odd $n$. Since $n...
We analyze divisibility by small primes:
Divisibility by 3**: Among any four consecutive odd integers, at least...
Divisibility by 5**: Not guaranteed — e.g., $n = 1$: $1 \cdot 3 \cdot...
Divisibility by higher powers or other primes?
Check powers of 3: Consider $n = 3$: $3 \cdot 5 \cdot 7 \cdot 9 = 945...
But $n = 9$: $9 \cdot 11 \cdot 13 \cdot 15 = 19305 = 3^3 \cdot 5 \cdot...

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