--description--

For a positive number $n$, define $S(n)$ as the sum of the integers $x$, for which $1 < x < n$ and $x^3 \equiv 1\bmod n$.

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 $S(13\,082\,761\,331\,670\,030)$.

--hints--

modularCubesOne() should return 4617456485273130000.

assert.strictEqual(modularCubesOne(), 4617456485273130000);

--seed--

--seed-contents--

function modularCubesOne() {

  return true;
}

modularCubesOne();

--solutions--

// solution required