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Home » The cross product \(\mathbfv \times \mathbfb\) is: - Tacotoon

The cross product \(\mathbfv \times \mathbfb\) is: - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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Now include the third congruence: \( k \equiv 2 \pmod{9} \)
Let \( k = 35b + 18 \). Then:
35b + 18 \equiv 2 \pmod{9}
Reduce modulo 9: \( 35 \equiv 8 \mod 9 \), \( 18 \equiv 0 \mod 9 \), s...
8b \equiv 2 \pmod{9}
Multiply both sides by the inverse of 8 modulo 9. Since \( 8 \cdot 8 =...
b \equiv 8 \cdot 2 = 16 \equiv 7 \pmod{9} \implies b = 9c + 7
k = 35(9c + 7) + 18 = 315c + 245 + 18 = 315c + 263
Thus, the smallest positive solution is when \( c = 0 \): \( k = 263 \...
The smallest such \( k \) is \( oxed{263} \).

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