47 lines
1.1 KiB
Markdown
47 lines
1.1 KiB
Markdown
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---
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id: 5900f5001000cf542c510012
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title: 'Problem 404: Crisscross Ellipses'
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challengeType: 5
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forumTopicId: 302072
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dashedName: problem-404-crisscross-ellipses
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---
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# --description--
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Ea is an ellipse with an equation of the form x2 + 4y2 = 4a2.
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Ea' is the rotated image of Ea by θ degrees counterclockwise around the origin O(0, 0) for 0° < θ < 90°.
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b is the distance to the origin of the two intersection points closest to the origin and c is the distance of the two other intersection points. We call an ordered triplet (a, b, c) a canonical ellipsoidal triplet if a, b and c are positive integers. For example, (209, 247, 286) is a canonical ellipsoidal triplet.
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Let C(N) be the number of distinct canonical ellipsoidal triplets (a, b, c) for a ≤ N. It can be verified that C(103) = 7, C(104) = 106 and C(106) = 11845.
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Find C(1017).
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# --hints--
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`euler404()` should return 1199215615081353.
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```js
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assert.strictEqual(euler404(), 1199215615081353);
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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 euler404() {
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return true;
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}
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euler404();
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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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