47 lines
897 B
Markdown
47 lines
897 B
Markdown
---
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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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It can also be verified that Q(3, 7) = 39590, Q(12, 3) = 309000 and Q(123, 45) = 70542215894646.
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Find Q(12345, 6789) mod 135707531.
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# --hints--
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`euler453()` should return 104354107.
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```js
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assert.strictEqual(euler453(), 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 euler453() {
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return true;
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}
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euler453();
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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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