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how do you restart a acer laptop - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 \sum_{k=1}^{10} k^3 = \left( \frac{10 \cdot 11}{2} \right)^2 = (55)^2 = 3025

📌 Now compute $ 3025 \mod 7 $. First, reduce 55 modulo 7:

📌 \div 7 = 7 \text{ remainder } 6 \Rightarrow 55 \equiv 6 \pmod{7}

📌 \Rightarrow 55^2 \equiv 6^2 = 36 \equiv 1 \pmod{7}

📌 Alternatively, $ 3025 \div 7 = 432 \text{ remainder } 1 $, so $ 3025 \equiv 1 \pmod{7} $.

📌 Therefore, the remainder is $ \boxed{1} $.

📌 Question: What is the greatest common divisor of $ 2^{12} - 1 $ and $ 2^{18} - 1 $?

📌 Solution: We use the identity:

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