d269909faa
* fix: clean-up Project Euler 381-400 * fix: missing image extension * fix: missing subscripts Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
45 lines
903 B
Markdown
45 lines
903 B
Markdown
---
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id: 5900f4f91000cf542c51000c
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title: 'Problem 397: Triangle on parabola'
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challengeType: 5
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forumTopicId: 302062
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dashedName: problem-397-triangle-on-parabola
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---
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# --description--
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On the parabola $y = \frac{x^2}{k}$, three points $A(a, \frac{a^2}{k})$, $B(b, \frac{b^2}{k})$ and $C(c, \frac{c^2}{k})$ are chosen.
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Let $F(K, X)$ be the number of the integer quadruplets $(k, a, b, c)$ such that at least one angle of the triangle $ABC$ is 45°, with $1 ≤ k ≤ K$ and $-X ≤ a < b < c ≤ X$.
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For example, $F(1, 10) = 41$ and $F(10, 100) = 12\\,492$.
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Find $F({10}^6, {10}^9)$.
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# --hints--
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`triangleOnParabola()` should return `141630459461893730`.
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```js
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assert.strictEqual(triangleOnParabola(), 141630459461893730);
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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 triangleOnParabola() {
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return true;
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}
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triangleOnParabola();
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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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