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illinois indiana college football playoff implications - ECD Germany

📅 May 15, 2026 👤 scraface

May 15, 2026

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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
Now compute \( 5025 \mod 11 \). Use alternating sum for modulo 11:
\( 5 - 0 + 2 - 5 = 2 \), or directly:
\( 5025 \div 11 \): \( 11 \times 456 = 5016 \), so \( 5025 - 5016 = 9...
Alternatively, each term mod 11:
\( 1001 \equiv 0 \pmod{11} \) (since \( 11 \times 91 = 1001 \))
\( 1003 \equiv 2 \)

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