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Putnam 1950 A6

Session A

Each coefficient $a_{n}$ of the power series $a_{0}+a_{1} x+a_{2} x^{2}+a_{3} x^{3}+\cdots=f(x)$ has either the value 1 or the value 0 . Prove the easier of the two assertions: (i) If $f(0.5)$ is a rational number, $f(x)$ is a rational function. (ii) If $f(0.5)$ is not a rational number, $f(x)$ is not a rational function.

Dataset text PutnamGAP. Quoted with source.

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