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robinette's apple haus and winery - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 What is the remainder when the sum \( 1^3 + 2^3 + 3^3 + \dots + 10^3 \) is divided by 11?

📌 We use the formula for the sum of cubes:

📌 Now compute \( 3025 \mod 11 \).

📌 First, reduce 55 modulo 11:

📌 \div 11 = 5 \quad \Rightarrow \quad 55 \equiv 0 \pmod{11}

📌 55^2 \equiv 0^2 = 0 \pmod{11}

📌 \equiv 0 \pmod{11}

📌 Therefore, the remainder is:

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