If gcd(a,n)=1, then the integers c,c+a,c+2a,c+3a,..,c+(n-1)a form a complete set of residues modulon

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If a_1,...,a_n is a complete set of residues mod n and gcd(a,n)=1 then aa_1,..., aa_n is complete . If a_1,...,a_n is a complete set of residues mod n and gcd(a,n)=1 then aa_1,..., aa_n is complete .
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