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Modular Cubes, part 2

Problem 272

Published on Saturday, 2nd January 2010, 05:00 am; Solved by 565; Difficulty rating: 80%

For a positive number n, define C(n) as the number 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, C(91)=8.

Find the sum of the positive numbers n≤1011 for which C(n)=242.