Difference between revisions of "Catalan's identity"
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(Created page with "==Theorem== The following formula holds: $$F_n^2 - F_{n+r} F_{n-r} = (-1)^{n-r}F_r^2,$$ where $F_n$ denotes a Fibonacci number. ==Proof== ==See also=...") |
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==Theorem== | ==Theorem== | ||
The following formula holds: | The following formula holds: | ||
| − | $$ | + | $$F(n)^2 - F(n+r) F(n-r) = (-1)^{n-r}F(r)^2,$$ |
| − | where $ | + | where $F(n)$ denotes the $n$th [[Fibonacci numbers|Fibonacci number]]. |
==Proof== | ==Proof== | ||
Latest revision as of 00:52, 25 May 2017
Theorem
The following formula holds: $$F(n)^2 - F(n+r) F(n-r) = (-1)^{n-r}F(r)^2,$$ where $F(n)$ denotes the $n$th Fibonacci number.
