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-y = x \quad extand \quad x = y - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 R(1) & = 6 \mod 17 = 6, \\

📌 R(3) & = 34 \equiv 0 \mod 17, \\

📌 R(4) & = 57 \equiv 57 - 3\times17 = 57 - 51 = 6 \mod 17, \\

📌 R(5) & = 86 \equiv 86 - 5\times17 = 86 - 85 = 1 \mod 17, \\

📌 R(6) & = 121 \equiv 121 - 7\times17 = 121 - 119 = 2 \mod 17, \\

📌 Since 17 divides \( R(3) \) and does not divide \( R(1), R(2), R(4), \ldots \), and the gcd must divide all values, but 17 does not divide all, we instead consider the gcd of the entire set.

📌 Compute \( \gcd(6, 17) = 1 \), since 6 and 17 are coprime. Any common divisor of all terms must divide 6 and 17. But \( \gcd(6, 17) = 1 \), so the overall gcd is 1.

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