A polynomial $\ f(x)$ has integer coefficients such that $\ f(0)$ and $\ f(1)$ are both odd numbers. Prove that $\ f(x) = 0$ has no integer solutions.

Asked May 14 '14 at 12:22

Active May 14 '14 at 12:53

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Let there be a polynomial $\ f(x)$. It has integer coefficients such that $\ f(0)$ and $\ f(1)$ are both odd numbers. Prove that $\ f(x) = 0$ has no integer solutions.

edited May 14 '14 at 12:26

Caleb Stanford

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asked May 14 '14 at 12:22

sourish

duplicate of http://math.stackexchange.com/q/753423/115115 and http://math.stackexchange.com/q/182593/115115 – Lutz Lehmann May 15 '14 at 09:01

A polynomial $\ f(x)$ has integer coefficients such that $\ f(0)$ and $\ f(1)$ are both odd numbers. Prove that $\ f(x) = 0$ has no integer solutions.

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