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Is it possible to compute the Moebius function without factoring?

Craig Alan Feinstein
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Abstract

It has been well known since Fermat's Little Theorem was first published that it is possible to determine that a number is composite without determining any of its nontrivial factors. It is natural to ask whether it is also possible to compute the Moebius function of a composite number without determining any of its nontrivial factors. In this note, we argue that this is impossible.

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Craig Alan Feinstein. 2011-12-14. Is it possible to compute the Moebius function without factoring?. https://arxiv.org/abs/math/0309148

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