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Topic: can someone point me to the proof that
Replies: 9   Last Post: Jul 24, 2013 10:39 AM

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Lax

Posts: 50
Registered: 3/18/07
Re: can someone point me to the proof that
Posted: Jul 21, 2013 5:49 PM
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On Sunday, July 21, 2013 5:43:22 PM UTC-4, Bart Goddard 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.
>
>
>
> 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.

I'll look up formal derivative :)



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