---
id: 5900f4551000cf542c50ff68
title: 'Problem 233: Lattice points on a circle'
challengeType: 5
forumTopicId: 301877
dashedName: problem-233-lattice-points-on-a-circle
---

# --description--

Let $f(N)$ be the number of points with integer coordinates that are on a circle passing through $(0,0)$, $(N,0)$,$(0,N)$, and $(N,N)$.

It can be shown that $f(10000) = 36$.

What is the sum of all positive integers $N ≤ {10}^{11}$ such that $f(N) = 420$?

# --hints--

`latticePointsOnACircle()` should return `271204031455541300`.

```js
assert.strictEqual(latticePointsOnACircle(), 271204031455541300);
```

# --seed--

## --seed-contents--

```js
function latticePointsOnACircle() {

  return true;
}

latticePointsOnACircle();
```

# --solutions--

```js
// solution required
```