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Putnam 2008 B5

Source:

December 8, 2008
Putnamfunctionnumber theorygreatest common divisorcalculusderivativeintegration

Problem Statement

Find all continuously differentiable functions f:R→R f: \mathbb{R}\to\mathbb{R} such that for every rational number q, q, the number f(q) f(q) is rational and has the same denominator as q. q. (The denominator of a rational number q q is the unique positive integer b b such that q\equal{}a/b for some integer a a with \gcd(a,b)\equal{}1.) (Note: gcd⁡ \gcd means greatest common divisor.)
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