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 prove

otherwise, but I don't see how this works. The problem

being 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 p

has zero constant term (hence p(t) = t q(t) for

some polynomial t and we're done, hence the

"not that it matters" above). How does

it 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_ of

the asspciated polynomial function. But..

>

>B.