## Modular Cubes, part 2

### Problem 272

Published on Saturday, 2nd January 2010, 05:00 am; Solved by 578; Difficulty rating: 80%
For a positive number `n`, define C(`n`) as the number 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, C(91)=8.

Find the sum of the positive numbers `n`≤10^{11} for which C(`n`)=242.