# Euler totien function

1. Feb 4, 2009

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.

2. 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. ////