I'm afraid this problem fits more to stackoverflow, but maybe it fits also here.
For a given $F_n$ (but we don't know $n$) find $F_{n-1}$, knowing that $\forall_{n>1}F_n=F_{n-1}+F_{n-2}$. Also $\forall_{n\in\mathbb{N}}F_n\in\mathbb{N}, \ F_{n+1}\ge F_{n}\ge 0$. I know, it's not clear, but we are looking for such number $F_{n-1}$ that $n$ is the highest. For example:
for $F_n = 10$; $F_{n-1}=6$
for $F_n = 17$; $F_{n-1}=11$
for $F_n = 4181$; $F_{n-1}=2584$
because for these values, number $n$ is the highest. I think it is a mathematical problem, but the answer can also be in the form of algorithm. Anyone has an idea how to find $F_{n-1}$ for a given $F_n$?
[EDIT]: when we can find more than one value of $F_{n-1}$ we have to chose this for which the value of $F_0$ is the lowest. I add this just in case. But I think it's not necessary, because my friend claims that it is not very hard to find $F_{n-1}$ and quite intuitive.