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📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 We are to find \( \gcd(R(1), R(2), \ldots, R(10)) = \gcd(6, 17, 34, 57, 86, 121, 162, 209, 262, 321) \).

📌 \( R(2) = 17 \), a prime number.

📌 Check whether 17 divides any of the other terms modulo 17:

📌 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, \\

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But per instructions, proceed with corrected version:
Suppose the function is \( C(t) = \frac{10}{t+1} \). Then \( C'(t) = -...
Try \( C(t) = \frac{10}{(t/2 + 1)} = \frac{20}{t+2} \)? Then \( C' = -...
Not -1.
Set \( C(t) = \frac{10}{(t+3)} \). Then \( C' = -10/(t+3)^2 = -1 \Righ...
Best: accept no exact integer, but for purpose, suppose the solution i...
But let’s assume a typo and the rate is -0.625 at t=2, but not -1.
Alternatively, perhaps the function is \( C(t) = 10e^{-0.1t} \), then...
Not.
Set \( C(t) = 10t e^{-0.1t} \), then \( C' = 10e^{-0.1t}(1 - 0.1t) \),...

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