47 lines
1.3 KiB
Markdown
47 lines
1.3 KiB
Markdown
---
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id: 5900f3f91000cf542c50ff0b
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title: 'Problem 141: Investigating progressive numbers, n, which are also square'
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challengeType: 5
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forumTopicId: 301770
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dashedName: problem-141-investigating-progressive-numbers-n-which-are-also-square
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---
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# --description--
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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.
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For example, 58 divided by 6 has a quotient of 9 and a remainder of 4. It can also be seen that 4, 6, 9 are consecutive terms in a geometric sequence (common ratio $\frac{3}{2}$).
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We will call such numbers, $n$, progressive.
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Some progressive numbers, such as 9 and 10404 = ${102}^2$, also happen to be perfect squares. The sum of all progressive perfect squares below one hundred thousand is 124657.
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Find the sum of all progressive perfect squares below one trillion (${101}^2$).
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# --hints--
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`progressivePerfectSquares()` should return `878454337159`.
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```js
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assert.strictEqual(progressivePerfectSquares(), 878454337159);
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```
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# --seed--
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## --seed-contents--
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```js
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function progressivePerfectSquares() {
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return true;
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}
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progressivePerfectSquares();
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```
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# --solutions--
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```js
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// solution required
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```
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