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Math Forum » Discussions » sci.math.* » sci.math.independent

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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Olivier

Posts: 27
Registered: 4/8/08
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 10:10 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.

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