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Home » Solution: To convert $ 321_8 $ to base ten, we expand it using powers of 8: - Crosslake

Solution: To convert $ 321_8 $ to base ten, we expand it using powers of 8: - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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Smallest positive \( N \) when \( c = 0 \): \( N = 67 \)
Check all conditions:
\( 67 \div 4 = 16 \times 4 = 64 \), remainder 3 → ✓
\( 67 \div 5 = 13 \times 5 = 65 \), remainder 2 → ✓
\( 67 \div 7 = 9 \times 7 = 63 \), remainder 4 → ✓
Thus, the smallest such \( N \) is:
\boxed{67}
An ornithologist analyzing flight data finds that the number of daily...
We seek the smallest three-digit integer \( D \) such that:
\( D^3 \equiv 1 \pmod{9} \), and

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