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Home » \( r = \sqrt[3]144 \approx 5.24 \) cm. - go-checkin.com

\( r = \sqrt[3]144 \approx 5.24 \) cm. - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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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...
But $n = 15$: $15 \cdot 17 \cdot 19 \cdot 21 = 3 \cdot 5 \cdot 17 \cdo...
But not always divisible by $81$ — try $n = 1$: only $3^1$. So maximum...
Now check if $3^3 = 27$ always divides $P$:

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