Residues of Mod problem.

MichaelG · #1 $Old$ November 2nd, 2009, 08:27 AM

If a1, a2....an is a complete set of residues modulo n and gcd(a,n)=1, prove that aa1, aa2...aan is also a complete set of residues modulo n

tonio · #2 $Old$ November 2nd, 2009, 08:53 AM

Quote:

Originally Posted by MichaelG $View Post$

If a1, a2....an is a complete set of residues modulo n and gcd(a,n)=1, prove that aa1, aa2...aan is also a complete set of residues modulo n

$aa_i=aa_k\Longrightarrow a(a_i-a_k)=xn\,,\,\,x\in \mathbb{Z}\Longrightarrow n\mid a(a_i-a_k)\,,\,\,but...$

Tonio