Möbius Inversion Formula for Arithmetic Functions

The Möbius inversion formula is an amazing result in number theory that allows us to recover a function from its summation function. This is an example of a phenomenon in math where partial information turns out to be enough to completely reconstructing the original object. A fair amount of machinery needs to be built (or in our video, assumed) to prove the inversion formula, but the result is well worth it. For example, it can be applied to derive an explicit formula for the Euler totient function, phi, without needing to resort to counting techniques like the principle of inclusion-exclusion.

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