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📅 May 1, 2026 👤 scraface

May 01, 2026

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📌 \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 \(\boxed{0}\).

📌 An emerging technology researcher exploring base systems in quantum computing asks: What is the base-ten number represented by the base-nine number \(321_9\)?

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