2018-10-10 22:03:03 +00:00
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---
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id: 5900f5001000cf542c510012
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2020-12-16 07:37:30 +00:00
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title: 问题404:交叉椭圆
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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-404-crisscross-ellipses
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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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Ea是椭圆,其形式为x2 + 4y2 = 4a2。 Ea'是Ea的旋转图像,绕原点O(0,0)逆时针旋转θ度0°<θ<90°。
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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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b是距离原点最近的两个交点的原点的距离,c是另外两个交点的距离。如果a,b和c是正整数,我们称有序三元组(a,b,c)为规范椭圆体三元组。例如,(209,247,286)是规范的椭圆体三重态。
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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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令C(N)为a≤N的不同规范椭球三胞胎(a,b,c)的数量。可以证实C(103)= 7,C(104)= 106和C(106)= 11845 。
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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C(1017)。
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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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`euler404()`应该返回1199215615081353。
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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(euler404(), 1199215615081353);
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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 euler404() {
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return true;
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}
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euler404();
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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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