email@example.com wrote in news:f6288bc3-b3b4-45bb-9425-2a70f2cea066 @googlegroups.com:
> no two polynomials are the same function over finite fields
I think you mean _infinite_ fields. In which case you can use functional methods. If the two polynomials give the same function, then plug 0 in for X to see that their constant terms are the same. Then take (formal) derivatives and plug in 0 again to see that the first-order coefficients are the same, etc.