yaworsw/euler-manager

---
:id: 403
:name: Lattice points enclosed by parabola and line
:url: https://projecteuler.net/problem=403
:content: "For integers <var>a</var> and <var>b</var>, we define <var>D</var>(<var>a</var>,
  <var>b</var>) as the domain enclosed by the parabola <var>y</var> = <var>x</var><sup>2</sup>
  and the line <var>y</var> = <var>a</var>·<var>x</var> + <var>b</var>:  \n<var>D</var>(<var>a</var>,
  <var>b</var>) = { (<var>x</var>, <var>y</var>) | <var>x</var><sup>2</sup> ≤ <var>y</var>
  ≤ <var>a</var>·<var>x</var> + <var>b</var> }.\n\nL(<var>a</var>, <var>b</var>) is
  defined as the number of lattice points contained in <var>D</var>(<var>a</var>,
  <var>b</var>).  \nFor example, L(1, 2) = 8 and L(2, -1) = 1.\n\nWe also define S(<var>N</var>)
  as the sum of L(<var>a</var>, <var>b</var>) for all the pairs (<var>a</var>, <var>b</var>)
  such that the area of <var>D</var>(<var>a</var>, <var>b</var>) is a rational number
  and |<var>a</var>|,|<var>b</var>| ≤ <var>N</var>.  \nWe can verify that S(5) = 344
  and S(100) = 26709528.\n\nFind S(10<sup>12</sup>). Give your answer mod 10<sup>8</sup>.\n\n"