MathDB

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 \plus{} 1\}, then F(0) \equal{} F(1) \equal{} \ldots \equal{} F(k \plus{} 1).

Problem Statement