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📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 x \equiv -1 \pmod{9} \quad \text{and} \quad x \equiv 1 \pmod{7}

📌 Rewriting:

📌 x = 9k - 1 \quad \text{for some } k

📌 Substitute into the second congruence:

📌 9k - 1 \equiv 1 \pmod{7} \Rightarrow 9k \equiv 2 \pmod{7}

📌 Since $ 9 \equiv 2 \pmod{7} $, this becomes:

📌 2k \equiv 2 \pmod{7} \Rightarrow k \equiv 1 \pmod{7}

📌 So $ k = 7m + 1 $, and:

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Compute GCD of $1119600$ and $60466176$.
So divide numerator and denominator by 432:
Check if $1119600$ divisible by $432$:
Subtract: $1,119,600 - 1,123,200 = -3,600$

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