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Modular Cubes, part 1

Problem 271

Published on Saturday, 2nd January 2010, 05:00 am; Solved by 1343

For a positive number n, define S(n) as the sum of the integers x, for which 1<x<n and
x3≡1 mod n.

When n=91, there are 8 possible values for x, namely : 9, 16, 22, 29, 53, 74, 79, 81.
Thus, S(91)=9+16+22+29+53+74+79+81=363.

Find S(13082761331670030).