Problem 271

Modular Cubes, part 1

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).

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