1.4 KiB
1.4 KiB
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°
.

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