Find all polynomials $p(x)$ satisfying condition Find all polynomials $p(x)$ such that $\sin{p(x)}$ is periodic.
I think that the condition for the solution is $\deg{p(x)}\le 1$, but i can't find a formal way to prove it.

You need to meet
$$p(x+T)=p(x)+2k\pi$$ or
$$p(x+T)-p(x)=2k\pi.$$ 
But for the LHS to be continuous, $k$ must be constant, hence $p(x)$ must indeed be linear.
