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id, title, challengeType, forumTopicId, dashedName
id title challengeType forumTopicId dashedName
5900f5001000cf542c510012 Problem 404: Crisscross Ellipses 5 302072 problem-404-crisscross-ellipses

--description--

E_a is an ellipse with an equation of the form x^2 + 4y^2 = 4a^2.

E_a' is the rotated image of E_a by θ degrees counterclockwise around the origin O(0, 0) for 0° < θ < 90°.

ellipse E_a and ellipse rotated by θ degrees E_a'

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({10}^3) = 7, C({10}^4) = 106 and C({10}^6) = 11\\,845.

Find C({10}^{17}).

--hints--

crisscrossEllipses() should return 1199215615081353.

assert.strictEqual(crisscrossEllipses(), 1199215615081353);

--seed--

--seed-contents--

function crisscrossEllipses() {

  return true;
}

crisscrossEllipses();

--solutions--

// solution required