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for all $ a, b, c \in \mathbbR $. - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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\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
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:

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