Talk:Fibonacci Number in terms of Larger Fibonacci Numbers

Might this be more elegantly expressed as:
 * $\forall m, n \in \Z_{>0} : \left({-1}\right)^n F_{m - n} = F_m F_{n - 1} - F_{m - 1} F_n$

?

Then you only have to keep track of one instance of the messy $\left({-1}\right)^n$ style of coefficient.

Also, would it be worth replacing this with d'Ocagne's identity:
 * $F_m F_{n+1} - F_{m+1} F_n = (-1)^n F_{m-n}$

which is so similar as to make little difference? It is derived from the above by putting $F_{(m+1)-(n+1)} = F_{m-n}$ and working from there. --prime mover (talk) 08:40, 20 November 2016 (EST)


 * I think minimizing the occurrence of $(-1)^n$ is a good a idea. Or, maybe better, make this one a corollary of d'Ocagne's. --GFauxPas (talk) 08:50, 20 November 2016 (EST)


 * D'Ocagne's Identity is already itself a corollary of $F_{m+n} = F_m F_{n+1} + F_{m-1} F_n$ so I wonder whether we need this specific result at all. Where it is used (in the proof of Vajda's identity) could be simplified if this simpler version were used. Or so I believe. --prime mover (talk) 08:56, 20 November 2016 (EST)