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Home » Find the radius of a circle if the circumference is equal to the area. - 500apps

Find the radius of a circle if the circumference is equal to the area. - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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R(8) &= 3(64) + 16 + 1 = 192 + 16 + 1 = 209, \\
R(9) &= 3(81) + 18 + 1 = 243 + 18 + 1 = 262, \\
R(10) &= 3(100) + 20 + 1 = 300 + 20 + 1 = 321.
We are to find \( \gcd(R(1), R(2), \ldots, R(10)) = \gcd(6, 17, 34, 57...
Notice:
\( R(2) = 17 \), 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, \\

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