Disprove the following: There exists a polynomial f(x) with integer coefficients such that f(1) is even and f(3) is odd.
The Attempt at a Solution
It's a little bit intuitive.
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?