freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-403-lattice-points-enclosed-by-parabola-and-line.md

id	title	challengeType	forumTopicId	dashedName
5900f5001000cf542c510013	Problem 403: Lattice points enclosed by parabola and line	5	302071	problem-403-lattice-points-enclosed-by-parabola-and-line

--description--

For integers a and b, we define D(a, b) as the domain enclosed by the parabola y = x^2 and the line y = ax + b: D(a, b) = \\{ (x, y) | x^2 ≤ y ≤ ax + b \\}.

L(a, b) is defined as the number of lattice points contained in D(a, b). For example, L(1, 2) = 8 and L(2, -1) = 1.

We also define S(N) as the sum of L(a, b) for all the pairs (a, b) such that the area of D(a, b) is a rational number and |a|,|b| ≤ N.

We can verify that S(5) = 344 and S(100) = 26\\,709\\,528.

Find S({10}^{12}). Give your answer \bmod {10}^8.

--hints--

latticePoints() should return 18224771.

assert.strictEqual(latticePoints(), 18224771);

--seed--

--seed-contents--

function latticePoints() {

  return true;
}

latticePoints();

--solutions--

// solution required