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≤F(c)≤k for each c\in \{0,1,\ldots,k \plus{} 1\}, then F(0) \equal{} F(1) \equal{} \ldots \equal{} F(k \plus{} 1). algebrapolynomialfunctional equationIMO Shortlist