55 lines
1.7 KiB
Markdown
55 lines
1.7 KiB
Markdown
---
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id: 5900f4fc1000cf542c51000e
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title: 'Problem 399: Squarefree Fibonacci Numbers'
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challengeType: 5
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forumTopicId: 302064
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dashedName: problem-399-squarefree-fibonacci-numbers
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---
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# --description--
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The first 15 fibonacci numbers are:
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1,1,2,3,5,8,13,21,34,55,89,144,233,377,610.
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It can be seen that 8 and 144 are not squarefree: 8 is divisible by 4 and 144 is divisible by 4 and by 9.
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So the first 13 squarefree fibonacci numbers are:
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1,1,2,3,5,13,21,34,55,89,233,377 and 610.
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The 200th squarefree fibonacci number is: 971183874599339129547649988289594072811608739584170445. The last sixteen digits of this number are: 1608739584170445 and in scientific notation this number can be written as 9.7e53.
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Find the 100 000 000th squarefree fibonacci number. Give as your answer its last sixteen digits followed by a comma followed by the number in scientific notation (rounded to one digit after the decimal point). For the 200th squarefree number the answer would have been: 1608739584170445,9.7e53
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Note: For this problem, assume that for every prime p, the first fibonacci number divisible by p is not divisible by p2 (this is part of Wall's conjecture). This has been verified for primes ≤ 3·1015, but has not been proven in general.
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If it happens that the conjecture is false, then the accepted answer to this problem isn't guaranteed to be the 100 000 000th squarefree fibonacci number, rather it represents only a lower bound for that number.
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# --hints--
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`euler399()` should return 1508395636674243, 6.5e27330467.
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```js
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assert.strictEqual(euler399(), 1508395636674243, 6.5e27330467);
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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 euler399() {
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return true;
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}
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euler399();
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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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