Eccoci.

The first $15$ Fibonacci numbers are:
$1,1,2,3,5,8,13,21,34,55,89,144,233,377,610$.
It can be seen that $8$ and $144$ are not squarefree: $8$ is divisible by $4$ and $144$ is divisible by $4$ and by $9$.
So the first $13$ squarefree Fibonacci numbers are:
$1,1,2,3,5,13,21,34,55,89,233,377$ and $610$.

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 $9.7\mathrm e53$.

Find the $100\,000\,000$th 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 $200$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 $\le 3 \cdot 10^{15}$, 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.