The $200$th 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`.
Find the $100\\,000\\,000$th squarefree fibonacci number. Give as your answer as a string with 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 $200$th squarefree number the answer would have been: `1608739584170445,9.7e53`
**Note:** For this problem, assume that for every prime $p$, the first fibonacci number divisible by $p$ is not divisible by $p^2$ (this is part of Wall's conjecture). This has been verified for primes $≤ 3 \times {10}^{15}$, but has not been proven in general.
If it happens that the conjecture is false, then the accepted answer to this problem isn't guaranteed to be the $100\\,000\\,000$th squarefree fibonacci number, rather it represents only a lower bound for that number.