Find all polynomials $P(x)$ with real coefficients such that $P(x)=P(x-1)$. Any elegant solutions to this somewhat (trivial?) question?
I think that since $P(x)=P(x-1)$ implies $P(x)=P(y)$ for all integers $x$ and $y$, $P(x)$ must be constant and also work for all reals. Is this valid? Any other solutions?