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Is there an explicit formula for the number of fourth powers mod n?

Finch & Sebah [1] give theorems, partially folklore, for squares and cubes mod n, but I don't know of a similar formula for higher powers.

[1] S. R. Finch and Pascal Sebah, Squares and Cubes Modulo n

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Reduce to the case $n$ is a prime power, then it's straightforward. – Geoff Robinson Aug 5 '11 at 18:50
@Geoff: Of course it's multiplicative by inspection (or the CRT, I suppose). – Charles Aug 6 '11 at 1:29
@Charles: Yes, by the CRT. Now add the fact that $\mathbb{Z}/n\mathbb{Z}$ has a simple structure when $n$ is a prime power (it is cyclic or the 2-element group times a cyclic group). – GH from MO Aug 8 '11 at 10:07

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