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Home » 3! This Cell Is So Perfect—You’ll Wonder How It’s Even Possible! - American Beagle Club

3! This Cell Is So Perfect—You’ll Wonder How It’s Even Possible! - American Beagle Club

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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We compute $ S = \sum_{k=1}^{9} k^3 \mod 9 $.
Use the formula for the sum of cubes:
For \( n = 9 \):
\sum_{k=1}^{9} k^3 = \left( \frac{9 \cdot 10}{2} \right)^2 = (45)^2 =...
Now compute \( 2025 \mod 9 \). A quick way: sum the digits of 2025:
+ 0 + 2 + 5 = 9 \Rightarrow 2025 \equiv 0 \mod 9.
Alternatively, note that \( 45 \equiv 0 \mod 9 \), so \( 45^2 \equiv 0...
Thus, the remainder is:
An epidemiologist analyzing cumulative case data finds a pattern where...
We seek the smallest positive integer \( n \) such that:

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