--- id: 5900f4f91000cf542c51000c title: 'Problem 397: Triangle on parabola' challengeType: 5 forumTopicId: 302062 dashedName: problem-397-triangle-on-parabola --- # --description-- On the parabola $y = \frac{x^2}{k}$, three points $A(a, \frac{a^2}{k})$, $B(b, \frac{b^2}{k})$ and $C(c, \frac{c^2}{k})$ are chosen. Let $F(K, X)$ be the number of the integer quadruplets $(k, a, b, c)$ such that at least one angle of the triangle $ABC$ is 45°, with $1 ≤ k ≤ K$ and $-X ≤ a < b < c ≤ X$. For example, $F(1, 10) = 41$ and $F(10, 100) = 12\\,492$. Find $F({10}^6, {10}^9)$. # --hints-- `triangleOnParabola()` should return `141630459461893730`. ```js assert.strictEqual(triangleOnParabola(), 141630459461893730); ``` # --seed-- ## --seed-contents-- ```js function triangleOnParabola() { return true; } triangleOnParabola(); ``` # --solutions-- ```js // solution required ```