Thread: 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!

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 , but so ...

Tonio