---
id: 5900f47d1000cf542c50ff8f
title: 'Problem 272: Modular Cubes, part 2'
challengeType: 5
forumTopicId: 301922
dashedName: problem-272-modular-cubes-part-2
---

# --description--

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

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

# --hints--

`modularCubesTwo()` should return `8495585919506151000`.

```js
assert.strictEqual(modularCubesTwo(), 8495585919506151000);
```

# --seed--

## --seed-contents--

```js
function modularCubesTwo() {

  return true;
}

modularCubesTwo();
```

# --solutions--

```js
// solution required
```