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## Homework Statement

Disprove the following: There exists a polynomial f(x) with integer coefficients such that f(1) is even and f(3) is odd.

## Homework Equations

## 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?