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Topic: n square free) ^ ( d I n and u = v (mod d) --> f(u) = f(v) (mod d) )
--> (f is a polynomial over Z_n)

Replies: 2   Last Post: Oct 16, 2009 3:37 PM

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Posts: 160
Registered: 11/29/05
Re: n square free) ^ ( d I n and u = v (mod d) --> f(u) = f(v) (mod
d) ) --> (f is a polynomial over Z_n)

Posted: Oct 16, 2009 3:37 PM
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On Oct 16, 10:10 am, Olivier <O...@nowhere.wd> wrote:
> G Patel a écrit :

> > How can I show that for any squarefree n and function f  from Z_n to
> > Z_n that has the propery that- whenever d I n and u = v (mod d) then f
> > (u) = f(v) (mod d) -  must be a polynomial over Z_n ?

> This is true when n is a prime.
> Use the chinese remainder Theorem.
> A.O.

is there a counterexample for when n is squarefree and not a prime?
how about when n is not squarefree?

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