66 lines
1.2 KiB
Markdown
66 lines
1.2 KiB
Markdown
---
|
|
id: 5900f5311000cf542c510044
|
|
challengeType: 5
|
|
title: 'Problem 453: Lattice Quadrilaterals'
|
|
forumTopicId: 302126
|
|
localeTitle: 'Задача 453: Квадратичные решетки'
|
|
---
|
|
|
|
## Description
|
|
<section id='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.
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>euler453()</code> should return 104354107.
|
|
testString: assert.strictEqual(euler453(), 104354107);
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function euler453() {
|
|
// Good luck!
|
|
return true;
|
|
}
|
|
|
|
euler453();
|
|
|
|
```
|
|
|
|
</div>
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
```js
|
|
// solution required
|
|
```
|
|
|
|
</section>
|