Math Help - Residues of Mod problem.

1. Residues of Mod problem.

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

2. Originally Posted by MichaelG
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

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

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