Problem 272

02 January 2010

For a positive number n, define C(n) as the number of the integers x, for which 1xn and
x³1 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 n10¹¹ for which C(n)=242.