In the proof reported in Aaron Grecius's notes on Euler’s Phi Function (p. 1) where is the fact that $(n,m)=1$ actually used ? I'm having trouble understanding it's significance.
2026-03-26 21:26:21.1774560381
What is the significance of $(n,m)=1$ in this proof that the Euler phi function is multiplicative?
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Its wrong otherwise, since e.g., $\phi(p^n) =(p-1)p^{n-1}$ and so $\phi(p^2) = (p-1)p$, but $\phi (p)\phi(p) =(p-1)^2$.