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* fix: clean-up Project Euler 121-140 * fix: corrections from review Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> * fix: missing backticks Co-authored-by: Kristofer Koishigawa <scissorsneedfoodtoo@gmail.com> * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> * fix: missing delimiter Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> Co-authored-by: Kristofer Koishigawa <scissorsneedfoodtoo@gmail.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
47 lines
1.3 KiB
Markdown
47 lines
1.3 KiB
Markdown
---
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id: 5900f3ee1000cf542c50ff00
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title: 'Problem 130: Composites with prime repunit property'
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challengeType: 5
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forumTopicId: 301758
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dashedName: problem-130-composites-with-prime-repunit-property
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---
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# --description--
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A number consisting entirely of ones is called a repunit. We shall define $R(k)$ to be a repunit of length $k$; for example, $R(6) = 111111$.
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Given that $n$ is a positive integer and $GCD(n, 10) = 1$, it can be shown that there always exists a value, $k$, for which $R(k)$ is divisible by $n$, and let $A(n)$ be the least such value of $k$; for example, $A(7) = 6$ and $A(41) = 5$.
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You are given that for all primes, $p > 5$, that $p − 1$ is divisible by $A(p)$. For example, when $p = 41, A(41) = 5$, and 40 is divisible by 5.
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However, there are rare composite values for which this is also true; the first five examples being 91, 259, 451, 481, and 703.
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Find the sum of the first twenty-five composite values of $n$ for which $GCD(n, 10) = 1$ and $n − 1$ is divisible by $A(n)$.
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# --hints--
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`compositeRepunit()` should return `149253`.
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```js
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assert.strictEqual(compositeRepunit(), 149253);
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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 compositeRepunit() {
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return true;
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}
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compositeRepunit();
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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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