Why is $$\sum_{d\mid n}\varphi(n/d)=\sum_{d\mid n}\varphi(d)$$
2026-04-01 06:06:04.1775023564
Why is $\sum_{d\mid n}\varphi(n/d)=\sum_{d\mid n}\varphi(d)$?
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Notice that $d\mapsto n/d$ is a bijection taking the set of divisors of n to itself. So both sides sum over the same terms.