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📅 May 18, 2026 👤 scraface

May 18, 2026

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For \( n = 12 \):
\sum_{k=1}^{12} k^3 = \left( \frac{12 \cdot 13}{2} \right)^2 = (78)^2...
Now compute \( 6084 \mod 9 \). Use digit sum or direct division:
Sum of digits of 6084: \( 6 + 0 + 8 + 4 = 18 \), and \( 18 \equiv 0 \p...
\equiv 0 \pmod{9}
Alternatively, \( 78 \equiv 78 \mod 9 \): \( 7 + 8 = 15 \Rightarrow 1...
Thus, the remainder is \( \boxed{0} \).
Question:** What is the remainder when \( 1001 + 1003 + 1005 + 1007 +...
Solution:** Compute the sum:
+ 1003 + 1005 + 1007 + 1009 = 5 \cdot 1005 = 5025

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