On Sunday, July 21, 2013 5:43:22 PM UTC-4, Bart Goddard wrote: > firstname.lastname@example.org 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. > > > > B.
Yes I meant infinite :)
What's funny is I did that proof above for F= reals or complex field, but then realized it was impossible for rationals.