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