926 B
926 B
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f5071000cf542c510018 | Problem 410: Circle and tangent line | 5 | 302079 | problem-410-circle-and-tangent-line |
--description--
Let C be the circle with radius r, x2 + y2 = r2. We choose two points P(a, b) and Q(-a, c) so that the line passing through P and Q is tangent to C.
For example, the quadruplet (r, a, b, c) = (2, 6, 2, -7) satisfies this property.
Let F(R, X) be the number of the integer quadruplets (r, a, b, c) with this property, and with 0 < r ≤ R and 0 < a ≤ X.
We can verify that F(1, 5) = 10, F(2, 10) = 52 and F(10, 100) = 3384. Find F(108, 109) + F(109, 108).
--hints--
euler410()
should return 799999783589946600.
assert.strictEqual(euler410(), 799999783589946600);
--seed--
--seed-contents--
function euler410() {
return true;
}
euler410();
--solutions--
// solution required