---
id: 5900f5311000cf542c510044
title: 'Problem 453: Lattice Quadrilaterals'
challengeType: 5
forumTopicId: 302126
dashedName: problem-453-lattice-quadrilaterals
---

# --description--

A simple quadrilateral is a polygon that has four distinct vertices, has no straight angles and does not self-intersect.

Let Q(m, n) be the number of simple quadrilaterals whose vertices are lattice points with coordinates (x,y) satisfying 0 ≤ x ≤ m and 0 ≤ y ≤ n.

For example, Q(2, 2) = 94 as can be seen below:

It can also be verified that Q(3, 7) = 39590, Q(12, 3) = 309000 and Q(123, 45) = 70542215894646.

Find Q(12345, 6789) mod 135707531.

# --hints--

`euler453()` should return 104354107.

```js
assert.strictEqual(euler453(), 104354107);
```

# --seed--

## --seed-contents--

```js
function euler453() {

  return true;
}

euler453();
```

# --solutions--

```js
// solution required
```
