Let $\displaystyle A$ be a finite comutative ring . If $\displaystyle f:A->A$ , $\displaystyle f(x)=X^2$ is injective prove that :

a) $\displaystyle 1+1=0 $

b) $\displaystyle P(x)=x^{2n}+a$ is reductible for all $\displaystyle n \in N$ and for all $\displaystyle a \in A $