7d9496e52c
* fix: clean-up Project Euler 361-380 * fix: improve wording Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> * fix: remove unnecessary paragraph * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
45 lines
805 B
Markdown
45 lines
805 B
Markdown
---
|
|
id: 5900f4e11000cf542c50fff3
|
|
title: 'Problem 372: Pencils of rays'
|
|
challengeType: 5
|
|
forumTopicId: 302034
|
|
dashedName: problem-372-pencils-of-rays
|
|
---
|
|
|
|
# --description--
|
|
|
|
Let $R(M, N)$ be the number of lattice points ($x$, $y$) which satisfy $M \lt x \le N$, $M \lt y \le N$ and $\left\lfloor\frac{y^2}{x^2}\right\rfloor$ is odd.
|
|
|
|
We can verify that $R(0, 100) = 3\\,019$ and $R(100, 10\\,000) = 29\\,750\\,422$.
|
|
|
|
Find $R(2 \times {10}^6, {10}^9)$.
|
|
|
|
**Note:** $\lfloor x\rfloor$ represents the floor function.
|
|
|
|
# --hints--
|
|
|
|
`pencilsOfRays()` should return `301450082318807040`.
|
|
|
|
```js
|
|
assert.strictEqual(pencilsOfRays(), 301450082318807040);
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function pencilsOfRays() {
|
|
|
|
return true;
|
|
}
|
|
|
|
pencilsOfRays();
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
// solution required
|
|
```
|