WakeUp wrote: Find all polynomials $P(x)$ with real coefficients such that \[(x-2010)P(x+67)=xP(x) \] for every integer $x$. result: $P(x)=C(x-2010)(x+1*67-2010)(x+2*67-2010)...(x-67)x$, $C=const$

$x|P(x+67)\to (x-67)|P(x)\to (x-67k)|P(x),k=1,2,...,30$. Therefore \[P(x)=P_1(x)\prod_{k=1}^{30}(x-67*k).\] And $P_1(x+67)=P_1(x)\to P_1(x)=const.$