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Home » Dark Type Agency Exposed: How Your Weakness Is Actually Your Greatest Secret - Sterling Industries

Dark Type Agency Exposed: How Your Weakness Is Actually Your Greatest Secret - Sterling Industries

📅 April 17, 2026 👤 scraface

Apr 17, 2026

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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}
\Rightarrow 55^2 \equiv 6^2 = 36 \equiv 1 \pmod{7}
Alternatively, $ 3025 \div 7 = 432 \text{ remainder } 1 $, so $ 3025 \...

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