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Euler totien function

  1. Feb 4, 2009 #1
    Q- Let m and n be coprime. Show that[tex]\phi[/tex](mn) = [tex]\phi[/tex](m) * [tex]\phi[/tex](n). Hint: when does a pair of residues modulo m and n have an inverse.
  2. jcsd
  3. Feb 4, 2009 #2
    [tex](\mathbf{Z}/mn\mathbf{Z})^{\times}=(\mathbf{Z}/m\mathbf{Z})^{\times}\times{(\mathbf{Z}/n\mathbf{Z})^{\times}}.[/tex] Take the orders of both sides. ////
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