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I'm asked to answer this question:

Let $f$ be a polynomial function not equal to zero, what can be said about $f(x)$ having $f(x-1)=f(x)$

Which has four choices, $f(x)$ is an odd or even or negative or positive function.

What I've done is finding out that $f(1)=f(0)$ and I'm stuck here.

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    @AndréNicolas: Thanks, that solves the problem as a complete answer.2012-01-23

1 Answers 1

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HINT: If $c$ is a zero of $f$, then so is $c-1$, $c-2$, ...

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    zizi, could you be more specific about what part you do $n$ot understand?2012-01-23