## Modular Cubes, part 1

### Problem 271

Published on Saturday, 2nd January 2010, 05:00 am; Solved by 1614; Difficulty rating: 60%
For a positive number `n`, define S(`n`) as the sum of the integers `x,` for which 1<`x`<`n` and`x`^{3}≡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).