49 lines
1.3 KiB
Markdown
49 lines
1.3 KiB
Markdown
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---
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id: 5900f5311000cf542c510044
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title: 'Problem 453: Lattice Quadrilaterals'
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challengeType: 5
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forumTopicId: 302126
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dashedName: problem-453-lattice-quadrilaterals
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---
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# --description--
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A simple quadrilateral is a polygon that has four distinct vertices, has no straight angles and does not self-intersect.
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Let $Q(m, n)$ be the number of simple quadrilaterals whose vertices are lattice points with coordinates ($x$, $y$) satisfying $0 ≤ x ≤ m$ and $0 ≤ y ≤ n$.
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For example, $Q(2, 2) = 94$ as can be seen below:
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<img class="img-responsive center-block" alt="94 quadrilaterals whose vertices are lattice points with coordinates (x, y) satiffying 0 ≤ x ≤ m and 0 ≤ y ≤ n" src="https://cdn.freecodecamp.org/curriculum/project-euler/lattice-quadrilaterals.png" style="background-color: white; padding: 10px;" />
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It can also be verified that $Q(3, 7) = 39\\,590$, $Q(12, 3) = 309\\,000$ and $Q(123, 45) = 70\\,542\\,215\\,894\\,646$.
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Find $Q(12\\,345, 6\\,789)\bmod 135\\,707\\,531$.
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# --hints--
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`latticeQuadrilaterals()` should return `104354107`.
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```js
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assert.strictEqual(latticeQuadrilaterals(), 104354107);
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```
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# --seed--
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## --seed-contents--
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```js
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function latticeQuadrilaterals() {
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return true;
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}
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latticeQuadrilaterals();
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```
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# --solutions--
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```js
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// solution required
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```
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