```Date: Jul 22, 2013 11:15 AM
Author: David C. Ullrich
Subject: Re: can someone point me to the proof that

On 21 Jul 2013 21:43:22 GMT, Bart Goddard <goddardbe@netscape.net>wrote:>lax.clarke@gmail.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.  Not that it matters, since the result is easy to proveotherwise, but I don't see how this works. The problembeing that the formal derivative is just "formal":Looking at the difference of our two polynomials,say p(t) = 0 for all t in our infinite field. So phas zero constant term (hence p(t) = t q(t) forsome polynomial t and we're done, hence the"not that it matters" above). How doesit follow that p'(t) = 0?That certainly follows for real or complex polynomials,since the formal derivative is also the derivative,with a definition in terms of the _values_ ofthe asspciated polynomial function. But..>>B.
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