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Home » \( 2(2w + 3) = 34 \) - Abu Waleed Tea

\( 2(2w + 3) = 34 \) - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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Since \( 20 \equiv 6 \equiv -1 \pmod{7} \), we have:
b \equiv 4 \pmod{7} \Rightarrow b \equiv -4 \equiv 3 \pmod{7}
So \( b = 7c + 3 \), then:
N = 20(7c + 3) + 7 = 140c + 60 + 7 = 140c + 67
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:

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