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

  1. #1
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    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.

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    Quote Originally Posted by NikoBellic View Post
    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 ...

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