What is the Euler Totient Function for Coprime Numbers?

Thread starter saadsarfraz
Start date Feb 4, 2009
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Euler Function

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The discussion focuses on proving that for coprime integers m and n, the Euler Totient Function satisfies the equation φ(mn) = φ(m) * φ(n). It highlights the importance of understanding when pairs of residues modulo m and n have inverses. The hint provided suggests utilizing the structure of the multiplicative group of integers modulo mn and its relation to the groups modulo m and n. Participants are encouraged to explore the orders of these groups to establish the proof. This foundational property of the Euler Totient Function is crucial in number theory.

Feb 4, 2009

saadsarfraz

Q- Let m and n be coprime. Show that\phi(mn) = \phi(m) * \phi(n). Hint: when does a pair of residues modulo m and n have an inverse.

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Feb 4, 2009

LorenzoMath

(\mathbf{Z}/mn\mathbf{Z})^{\times}=(\mathbf{Z}/m\mathbf{Z})^{\times}\times{(\mathbf{Z}/n\mathbf{Z})^{\times}}. Take the orders of both sides. ////

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