yaworsw/euler-manager

---
:id: 397
:name: Triangle on parabola
:url: https://projecteuler.net/problem=397
:content: "On the parabola <var>y</var> = <var>x</var><sup>2</sup>/<var>k</var>, three
  points A(<var>a</var>, <var>a</var><sup>2</sup>/<var>k</var>), B(<var>b</var>, <var>b</var><sup>2</sup>/<var>k</var>)
  and C(<var>c</var>, <var>c</var><sup>2</sup>/<var>k</var>) are chosen.\n\nLet F(<var>K</var>,
  <var>X</var>) be the number of the integer quadruplets (<var>k</var>, <var>a</var>,
  <var>b</var>, <var>c</var>) such that at least one angle of the triangle ABC is
  45-degree, with 1 ≤ <var>k</var> ≤ <var>K</var> and -<var>X</var> ≤ <var>a</var>
  \\< <var>b</var> \\< <var>c</var> ≤ <var>X</var>.\n\nFor example, F(1, 10) = 41
  and F(10, 100) = 12492.  \nFind F(10<sup>6</sup>, 10<sup>9</sup>).\n\n"