61 lines
958 B
Markdown
61 lines
958 B
Markdown
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---
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id: 5900f5311000cf542c510042
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title: 'Problem 451: Modular inverses'
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challengeType: 5
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forumTopicId: 302124
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dashedName: problem-451-modular-inverses
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---
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# --description--
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Consider the number 15.
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There are eight positive numbers less than 15 which are coprime to 15: 1, 2, 4, 7, 8, 11, 13, 14.
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The modular inverses of these numbers modulo 15 are: 1, 8, 4, 13, 2, 11, 7, 14
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because
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1\*1 mod 15=1
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2\*8=16 mod 15=1
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4\*4=16 mod 15=1
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7\*13=91 mod 15=1
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11\*11=121 mod 15=1
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14\*14=196 mod 15=1
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Let I(n) be the largest positive number m smaller than n-1 such that the modular inverse of m modulo n equals m itself. So I(15)=11. Also I(100)=51 and I(7)=1.
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Find ∑I(n) for 3≤n≤2·107
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# --hints--
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`euler451()` should return 153651073760956.
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```js
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assert.strictEqual(euler451(), 153651073760956);
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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 euler451() {
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return true;
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}
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euler451();
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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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