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Product of the Euler phi function [duplicate]
Prove the following statement: If $n, m\in\mathbb{Z} $ and $g=$gcd$(n, m) $ then is
$$\varphi(m, n) =\frac{ \varphi(m) \varphi(n) g} {\varphi(g)}. $$
Hint: Prove the statement with induction above ...
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