How many positive integer $(n < 180)$ that$ (n^3 + 3n+1)^{180} (mod 180) = 1 $?

by ABCDEFG user157844   Last Updated June 12, 2019 08:20 AM

How can we manage a large exponent and set it to a perfect square or something?

I only started with $n^3 + 3n \equiv 0 \ mod \ 180 \ $ and $n^3 + 3n \equiv -2 \ mod \ 180 \ $

but it seems not sure that coverage all of answers or not.

If I have deal with $(n^3 + 3n+1)^{36} \equiv 1 \ mod \ 180 \ $I can't transform it to a perfect cube.

I'm appreciate for your help.



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