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📅 March 6, 2026 👤 scraface

Mar 06, 2026

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🔥 Popular Posts

5k - 3 \leq 100 \Rightarrow 5k \leq 103 \Rightarrow k \leq \frac{103}{...
Thus, $ k = 1, 2, \dots, 20 $, so there are 20 such numbers.
Therefore, the number of integers is $ \boxed{20} $.
Question: What is the remainder when the sum $ 1^3 + 2^3 + 3^3 + \dots...
Solution: We use the formula for the sum of cubes:
\sum_{k=1}^{n} k^3 = \left( \frac{n(n+1)}{2} \right)^2
For $ n = 10 $:
\sum_{k=1}^{10} k^3 = \left( \frac{10 \cdot 11}{2} \right)^2 = (55)^2...
Now compute $ 3025 \mod 7 $. First, reduce 55 modulo 7:
\div 7 = 7 \text{ remainder } 6 \Rightarrow 55 \equiv 6 \pmod{7}

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