Math Help - Prove that... complete set of residues mod m.

1. Prove that... complete set of residues mod m.

Let a1, a2, ..., am be a complete set of residues mod m [that is, they represent all the different classes mod m]. Take k with gcd(k,m)=1 and any integer b. Prove that the numbers ka1+b, ka2+b, ..., kam+b are another complete set of residues mod m.

Thanks!

2. Originally Posted by NikoBellic
Let a1, a2, ..., am be a complete set of residues mod m [that is, they represent all the different classes mod m]. Take k with gcd(k,m)=1 and any integer b. Prove that the numbers ka1+b, ka2+b, ..., kam+b are another complete set of residues mod m.

Thanks!

Suppose $ka_i+b=ka_j+b\!\!\!\pmod m\Longrightarrow k(a_i-a_j)=0\!\!\!\pmod m$ , but $(k,m)=1$ so ...

Tonio