2018-10-10 22:03:03 +00:00
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---
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id: 5900f5311000cf542c510044
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2020-12-16 07:37:30 +00:00
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title: 问题453:格子四边形
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2018-10-10 22:03:03 +00:00
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challengeType: 5
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videoUrl: ''
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2021-01-13 02:31:00 +00:00
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dashedName: problem-453-lattice-quadrilaterals
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2018-10-10 22:03:03 +00:00
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---
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2020-12-16 07:37:30 +00:00
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# --description--
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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简单的四边形是具有四个不同顶点的多边形,没有直角并且不会自相交。
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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设Q(m,n)为简单四边形的数量,其顶点为格点,坐标(x,y)满足0≤x≤m且0≤y≤n。
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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例如,Q(2,2)= 94,如下所示:
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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还可以证实Q(3,7)= 39590,Q(12,3)= 309000和Q(123,45)= 70542215894646。
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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找到Q(12345,6789)mod 135707531。
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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# --hints--
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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`euler453()`应该返回104354107。
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2018-10-10 22:03:03 +00:00
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```js
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2020-12-16 07:37:30 +00:00
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assert.strictEqual(euler453(), 104354107);
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2018-10-10 22:03:03 +00:00
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```
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2021-01-13 02:31:00 +00:00
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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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2020-12-16 07:37:30 +00:00
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# --solutions--
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2020-08-13 15:24:35 +00:00
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2021-01-13 02:31:00 +00:00
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```js
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// solution required
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```
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