57 lines
1.2 KiB
Markdown
57 lines
1.2 KiB
Markdown
---
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id: 5900f4461000cf542c50ff59
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title: 'Problem 218: Perfect right-angled triangles'
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challengeType: 5
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forumTopicId: 301860
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dashedName: problem-218-perfect-right-angled-triangles
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---
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# --description--
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Consider the right-angled triangle with sides $a=7$, $b=24$ and $c=25$.
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The area of this triangle is 84, which is divisible by the perfect numbers 6 and 28.
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Moreover it is a primitive right-angled triangle as $gcd(a,b) = 1$ and $gcd(b,c) = 1$.
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Also $c$ is a perfect square.
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We will call a right-angled triangle perfect if:
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- it is a primitive right-angled triangle
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- its hypotenuse is a perfect square
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We will call a right-angled triangle super-perfect if:
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- it is a perfect right-angled triangle
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- its area is a multiple of the perfect numbers 6 and 28.
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How many perfect right-angled triangles with $c ≤ {10}^{16}$ exist that are not super-perfect?
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# --hints--
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`perfectRightAngledTriangles()` should return `0`.
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```js
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assert.strictEqual(perfectRightAngledTriangles(), 0);
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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 perfectRightAngledTriangles() {
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return true;
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}
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perfectRightAngledTriangles();
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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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