47 lines
873 B
Markdown
47 lines
873 B
Markdown
---
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id: 5900f51d1000cf542c51002f
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title: 'Problem 433: Steps in Euclid''s algorithm'
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challengeType: 5
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forumTopicId: 302104
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dashedName: problem-433-steps-in-euclids-algorithm
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---
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# --description--
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Let E(x0, y0) be the number of steps it takes to determine the greatest common divisor of x0 and y0 with Euclid's algorithm. More formally:x1 = y0, y1 = x0 mod y0xn = yn-1, yn = xn-1 mod yn-1
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E(x0, y0) is the smallest n such that yn = 0.
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We have E(1,1) = 1, E(10,6) = 3 and E(6,10) = 4.
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Define S(N) as the sum of E(x,y) for 1 ≤ x,y ≤ N. We have S(1) = 1, S(10) = 221 and S(100) = 39826.
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Find S(5·106).
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# --hints--
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`euler433()` should return 326624372659664.
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```js
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assert.strictEqual(euler433(), 326624372659664);
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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 euler433() {
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return true;
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}
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euler433();
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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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