Let be a finite comutative ring . If , is injective prove that :
b) is reductible for all and for all
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Convince yourself that and it follows (because f is injective) that or equivalently 1+1=0.
Part b) is a bit trickier.
f is injective so there exists such that . Hence is exists.
Part a) shows that A has characteristic 2 and hence
Ta da. P(x) is reducible
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