yaworsw/euler-manager

---
:id: 399
:name: Squarefree Fibonacci Numbers
:url: https://projecteuler.net/problem=399
:content: "The first 15 fibonacci numbers are:  \n1,1,2,3,5,8,13,21,34,55,89,144,233,377,610.
  \ \nIt can be seen that 8 and 144 are not squarefree: 8 is divisible by 4 and 144
  is divisible by 4 and by 9.  \n So the first 13 squarefree fibonacci numbers are:
  \ \n1,1,2,3,5,13,21,34,55,89,233,377 and 610.\n\nThe 200th squarefree fibonacci
  number is: 971183874599339129547649988289594072811608739584170445.  \nThe last sixteen
  digits of this number are: 1608739584170445 and in scientific notation this number
  can be written as 9.7e53.\n\nFind the 100 000 000th squarefree fibonacci number.
  \ \nGive 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).
  \ \nFor the 200th squarefree number the answer would have been: 1608739584170445,9.7e53\n\n<font
  size=\"-1\">\nNote:<br> \nFor this problem, assume that for every prime p, the first
  fibonacci number divisible by p is not divisible by p<sup>2</sup> (this is part
  of <b>Wall's conjecture</b>). This has been verified for primes ≤ 3·10<sup>15</sup>,
  but has not been proven in general.<br>\n\nIf 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.\n</font>\n\n"