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Home » Since it's not, **no such \(\mathbfv\) exists**. - Crosslake

Since it's not, no such \(\mathbfv\) exists. - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 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.

📌 Therefore, the greatest common divisor of all \( R(t) \) for \( t = 1 \) to \( 10 \) is:

📌 An epidemiologist tracking a disease outbreak observes that the total number of cases over two consecutive weeks is 144, and the greatest common divisor of the weekly case counts is as large as possible. What is the largest possible value of \( \gcd(a, b) \) if \( a + b = 144 \) and \( a, b \) are positive integers?

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