47 lines
1.2 KiB
Markdown
47 lines
1.2 KiB
Markdown
---
|
|
id: 5900f3f91000cf542c50ff0b
|
|
title: 'Problem 141: Investigating progressive numbers, n, which are also square'
|
|
challengeType: 5
|
|
forumTopicId: 301770
|
|
dashedName: problem-141-investigating-progressive-numbers-n-which-are-also-square
|
|
---
|
|
|
|
# --description--
|
|
|
|
A positive integer, n, is divided by d and the quotient and remainder are q and r respectively. In addition d, q, and r are consecutive positive integer terms in a geometric sequence, but not necessarily in that order.
|
|
|
|
For example, 58 divided by 6 has quotient 9 and remainder 4. It can also be seen that 4, 6, 9 are consecutive terms in a geometric sequence (common ratio 3/2).
|
|
|
|
We will call such numbers, n, progressive.
|
|
|
|
Some progressive numbers, such as 9 and 10404 = 1022, happen to also be perfect squares. The sum of all progressive perfect squares below one hundred thousand is 124657.
|
|
|
|
Find the sum of all progressive perfect squares below one trillion (1012).
|
|
|
|
# --hints--
|
|
|
|
`euler141()` should return 878454337159.
|
|
|
|
```js
|
|
assert.strictEqual(euler141(), 878454337159);
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function euler141() {
|
|
|
|
return true;
|
|
}
|
|
|
|
euler141();
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
// solution required
|
|
```
|