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Home » Burgundy Dress Revealed—This Color Rules Every Season This Fall! - Sterling Industries

Burgundy Dress Revealed—This Color Rules Every Season This Fall! - Sterling Industries

📅 April 18, 2026 👤 scraface

Apr 18, 2026

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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:

📌 \(55 \div 11 = 5\), so \(55 \equiv 0 \pmod{11}\).

📌 Then \(55^2 \equiv 0^2 = 0 \pmod{11}\).

📌 Thus, \(3025 \equiv 0 \pmod{11}\).

📌 Alternatively, since \(55 \equiv 0 \mod 11\), the square is divisible by \(11^2\), hence by 11.

📌 Therefore, the remainder is \(\boxed{0}\).

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