Find all positive integers
for which the following statement is true: If
is a polynomial with integer coefficients satisfying the condition
for each
, then
.
%V0
Find all positive integers $k$ for which the following statement is true: If $F(x)$ is a polynomial with integer coefficients satisfying the condition $0 \leq F(c) \leq k$ for each $c\in \{0,1,\ldots,k + 1\}$, then $F(0) = F(1) = \ldots = F(k + 1)$.
Školjka