2018-10-10 22:03:03 +00:00
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---
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id: 5900f51d1000cf542c51002f
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2020-12-16 07:37:30 +00:00
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title: 问题433:欧几里得算法的步骤
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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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---
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2020-12-16 07:37:30 +00:00
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# --description--
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2020-02-17 16:40:55 +00:00
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设E(x0,y0)为用Euclid算法确定x0和y0的最大公约数所需要的步数。 更正式地说:x1 = y0,y1 = x0 mod y0xn = yn-1,yn = xn-1 mod yn-1
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2020-12-16 07:37:30 +00:00
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E(x0,y0)是最小的n,因此yn = 0。
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2020-02-17 16:40:55 +00:00
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我们有E(1,1)= 1,E(10,6)= 3和E(6,10)= 4。
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2020-12-16 07:37:30 +00:00
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将S(N)定义为1≤x,y≤N的E(x,y)之和。 我们有S(1)= 1,S(10)= 221和S(100)= 39826。
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2020-02-17 16:40:55 +00:00
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求S(5·106)。
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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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`euler433()`应该返回326624372659664。
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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(euler433(), 326624372659664);
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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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# --solutions--
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2020-08-13 15:24:35 +00:00
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