chore(i8n,learn): processed translations
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Mrugesh Mohapatra
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---
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id: 5900f5241000cf542c510037
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title: 问题440:GCD和平铺
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title: 'Problem 440: GCD and Tiling'
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challengeType: 5
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videoUrl: ''
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forumTopicId: 302112
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dashedName: problem-440-gcd-and-tiling
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---
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# --description--
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我们要完全平铺一块长度为n且高度为1的板,上面有1×2块或1×1块,上面有一个十进制数字:
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We want to tile a board of length n and height 1 completely, with either 1 × 2 blocks or 1 × 1 blocks with a single decimal digit on top:
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例如,以下是铺砌长度为n = 8的板的一些方法:
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For example, here are some of the ways to tile a board of length n = 8:
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令T(n)是如上所述的平铺长度为n的板的方式的数量。
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Let T(n) be the number of ways to tile a board of length n as described above.
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例如,T(1)= 10且T(2)= 101。
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For example, T(1) = 10 and T(2) = 101.
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令S(L)为1≤a,b,c≤L的三次和∑a,b,c gcd(T(ca),T(cb))。 例如: S(2)= 10444 S(3)= 1292115238446807016106539989 S(4)模数987898789 = 670616280。
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Let S(L) be the triple sum ∑a,b,c gcd(T(ca), T(cb)) for 1 ≤ a, b, c ≤ L. For example: S(2) = 10444 S(3) = 1292115238446807016106539989 S(4) mod 987 898 789 = 670616280.
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找出S(2000)mod 987898898。
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Find S(2000) mod 987 898 789.
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# --hints--
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`euler440()`应该返回970746056。
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`euler440()` should return 970746056.
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```js
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assert.strictEqual(euler440(), 970746056);
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