1. The problem statement, all variables and given/known data Disprove the following: There exists a polynomial f(x) with integer coefficients such that f(1) is even and f(3) is odd. 2. Relevant equations 3. The attempt at a solution It's a little bit intuitive. Proof 1 and 3 have the same parity. They are both odd so if(odd)=odd then f(1)=odd and f(3)=odd or if(odd)=even then f(1)=even and f(3)=even is that right?