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id	title	challengeType	forumTopicId	dashedName
5900f5311000cf542c510044	Problem 453: Lattice Quadrilaterals	5	302126	problem-453-lattice-quadrilaterals

--description--

A simple quadrilateral is a polygon that has four distinct vertices, has no straight angles and does not self-intersect.

Let Q(m, n) be the number of simple quadrilaterals whose vertices are lattice points with coordinates (x, y) satisfying 0 ≤ x ≤ m and 0 ≤ y ≤ n.

For example, Q(2, 2) = 94 as can be seen below:

94 quadrilaterals whose vertices are lattice points with coordinates (x, y) satiffying 0 ≤ x ≤ m and 0 ≤ y ≤ n

It can also be verified that Q(3, 7) = 39\\,590, Q(12, 3) = 309\\,000 and Q(123, 45) = 70\\,542\\,215\\,894\\,646.

Find Q(12\\,345, 6\\,789)\bmod 135\\,707\\,531.

--hints--

latticeQuadrilaterals() should return 104354107.

assert.strictEqual(latticeQuadrilaterals(), 104354107);

--seed--

--seed-contents--

function latticeQuadrilaterals() {

  return true;
}

latticeQuadrilaterals();

--solutions--

// solution required

1.3 KiB Raw Blame History