2018-10-10 18:03:03 -04:00
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---
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id: 5900f4f21000cf542c510005
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2020-12-16 00:37:30 -07:00
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title: 问题390:具有非理性边和积分面积的三角形
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2018-10-10 18:03:03 -04:00
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challengeType: 5
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videoUrl: ''
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2021-01-13 03:31:00 +01:00
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dashedName: problem-390-triangles-with-non-rational-sides-and-integral-area
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2018-10-10 18:03:03 -04:00
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---
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2020-12-16 00:37:30 -07:00
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# --description--
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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考虑边长为√5,√65和√68的三角形。可以看出,该三角形具有区域9。
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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S(n)是所有三角形的面积之和,其边长为√(1 + b2),√(1 + c2)和√(b2 + c2)(对于正整数b和c),其积分面积不超过ñ。
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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示例三角形的b = 2且c = 8。
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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S(106)= 18018206。
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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找到S(1010)。
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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# --hints--
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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`euler390()`应该返回2919133642971。
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2018-10-10 18:03:03 -04:00
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```js
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2020-12-16 00:37:30 -07:00
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assert.strictEqual(euler390(), 2919133642971);
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2018-10-10 18:03:03 -04:00
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```
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2021-01-13 03:31:00 +01:00
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# --seed--
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## --seed-contents--
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```js
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function euler390() {
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return true;
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}
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euler390();
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```
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2020-12-16 00:37:30 -07:00
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# --solutions--
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2020-08-13 17:24:35 +02:00
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2021-01-13 03:31:00 +01:00
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```js
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// solution required
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```
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