---
id: 5900f4f11000cf542c510002
title: 'Problem 388: Distinct Lines'
challengeType: 5
forumTopicId: 302052
dashedName: problem-388-distinct-lines
---

# --description--

Consider all lattice points ($a$, $b$, $c$) with $0 ≤ a, b, c ≤ N$.

From the origin $O(0, 0, 0)$ all lines are drawn to the other lattice points. Let $D(N)$ be the number of distinct such lines.

You are given that $D(1\\,000\\,000) = 831\\,909\\,254\\,469\\,114\\,121$.

Find $D({10}^{10})$. Give as your answer the first nine digits followed by the last nine digits.

# --hints--

`distinctLines()` should return `831907372805130000`.

```js
assert.strictEqual(distinctLines(), 831907372805130000);
```

# --seed--

## --seed-contents--

```js
function distinctLines() {

  return true;
}

distinctLines();
```

# --solutions--

```js
// solution required
```