45 lines
835 B
Markdown
45 lines
835 B
Markdown
|
---
|
|||
|
|
id: 5900f3f51000cf542c50ff07
|
|||
|
|
title: 'Problem 136: Singleton difference'
|
|||
|
|
challengeType: 5
|
|||
|
|
forumTopicId: 301764
|
|||
|
|
dashedName: problem-136-singleton-difference
|
|||
|
|
---
|
|||
|
|
|
|||
|
|
# --description--
|
|||
|
|
|
|||
|
|
The positive integers, x, y, and z, are consecutive terms of an arithmetic progression. Given that n is a positive integer, the equation, x2 − y2 − z2 = n, has exactly one solution when n = 20:
|
|||
|
|
|
|||
|
|
132 − 102 − 72 = 20
|
|||
|
|
|
|||
|
|
In fact there are twenty-five values of n below one hundred for which the equation has a unique solution.
|
|||
|
|
|
|||
|
|
How many values of n less than fifty million have exactly one solution?
|
|||
|
|
|
|||
|
|
# --hints--
|
|||
|
|
|
|||
|
|
`euler136()` should return 2544559.
|
|||
|
|
|
|||
|
|
```js
|
|||
|
|
assert.strictEqual(euler136(), 2544559);
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
# --seed--
|
|||
|
|
|
|||
|
|
## --seed-contents--
|
|||
|
|
|
|||
|
|
```js
|
|||
|
|
function euler136() {
|
|||
|
|
|
|||
|
|
return true;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
euler136();
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
# --solutions--
|
|||
|
|
|
|||
|
|
```js
|
|||
|
|
// solution required
|
|||
|
|
```
|