1.1 KiB
1.1 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f5001000cf542c510012 | Problem 404: Crisscross Ellipses | 5 | 302072 | problem-404-crisscross-ellipses |
--description--
Ea is an ellipse with an equation of the form x2 + 4y2 = 4a2.
Ea' is the rotated image of Ea by θ degrees counterclockwise around the origin O(0, 0) for 0° < θ < 90°.
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.
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.
Find C(1017).
--hints--
euler404()
should return 1199215615081353.
assert.strictEqual(euler404(), 1199215615081353);
--seed--
--seed-contents--
function euler404() {
return true;
}
euler404();
--solutions--
// solution required