Let
be a prime number and
an integer polynomial of degree
such that
and
is congruent to
or
modulo
for every integer
. Prove that
.
%V0
Let $p$ be a prime number and $f$ an integer polynomial of degree $d$ such that $f(0) = 0,f(1) = 1$ and $f(n)$ is congruent to $0$ or $1$ modulo $p$ for every integer $n$. Prove that $d\geq p - 1$.
Školjka