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A geneticist analyzing periodic patterns in modular arithmetic asks: What is the remainder when the sum \(1^3 + 2^3 + 3^3 + \cdots + 10^3\) is divided by 11?
\sum_{k=1}^{10} k^3 = \left( \frac{10 \times 11}{2} \right)^2 = (55)^2 = 3025
Now compute \(3025 \mod 11\). First, reduce 55 modulo 11:

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