Question 60
Let $P(x), Q(x)$ be nonconstant polynomials with real number coefficients. Prove that if
$$
\lfloor P(y)\rfloor=\lfloor Q(y)\rfloor
$$
for all real numbers $y$, then $P(x)=Q(x)$ for all real numbers $x$.
$$
\lfloor P(y)\rfloor=\lfloor Q(y)\rfloor
$$
for all real numbers $y$, then $P(x)=Q(x)$ for all real numbers $x$.