69 lines
1.1 KiB
Markdown
69 lines
1.1 KiB
Markdown
|
---
|
||
|
id: 5900f5001000cf542c510013
|
||
|
challengeType: 5
|
||
|
title: 'Problem 403: Lattice points enclosed by parabola and line'
|
||
|
forumTopicId: 302071
|
||
|
---
|
||
|
|
||
|
## Description
|
||
|
<section id='description'>
|
||
|
For integers a and b, we define D(a, b) as the domain enclosed by the parabola y = x2 and the line y = a·x + b:D(a, b) = { (x, y) | x2 ≤ y ≤ a·x + b }.
|
||
|
|
||
|
|
||
|
L(a, b) is defined as the number of lattice points contained in D(a, b).
|
||
|
For example, L(1, 2) = 8 and L(2, -1) = 1.
|
||
|
|
||
|
|
||
|
We also define S(N) as the sum of L(a, b) for all the pairs (a, b) such that the area of D(a, b) is a rational number and |a|,|b| ≤ N.
|
||
|
We can verify that S(5) = 344 and S(100) = 26709528.
|
||
|
|
||
|
|
||
|
Find S(1012). Give your answer mod 108.
|
||
|
</section>
|
||
|
|
||
|
## Instructions
|
||
|
<section id='instructions'>
|
||
|
|
||
|
</section>
|
||
|
|
||
|
## Tests
|
||
|
<section id='tests'>
|
||
|
|
||
|
```yml
|
||
|
tests:
|
||
|
- text: <code>euler403()</code> should return 18224771.
|
||
|
testString: assert.strictEqual(euler403(), 18224771);
|
||
|
|
||
|
```
|
||
|
|
||
|
</section>
|
||
|
|
||
|
## Challenge Seed
|
||
|
<section id='challengeSeed'>
|
||
|
|
||
|
<div id='js-seed'>
|
||
|
|
||
|
```js
|
||
|
function euler403() {
|
||
|
|
||
|
return true;
|
||
|
}
|
||
|
|
||
|
euler403();
|
||
|
```
|
||
|
|
||
|
</div>
|
||
|
|
||
|
|
||
|
|
||
|
</section>
|
||
|
|
||
|
## Solution
|
||
|
<section id='solution'>
|
||
|
|
||
|
```js
|
||
|
// solution required
|
||
|
```
|
||
|
|
||
|
</section>
|