Difference between revisions of "L(n+1)L(n-1)-L(n)^2=5(-1)^(n+1)"
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(Created page with "==Theorem== The following formula holds: $$L(n+1)L(n-1)-L(n)^2=5(-1)^{n+1},$$ where $L(n)$ denotes a Lucas number. ==Proof== ==References== * {{PaperReference|A Primer o...") |
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The following formula holds: | The following formula holds: | ||
$$L(n+1)L(n-1)-L(n)^2=5(-1)^{n+1},$$ | $$L(n+1)L(n-1)-L(n)^2=5(-1)^{n+1},$$ | ||
| − | where $L(n)$ denotes a [[Lucas number]]. | + | where $L(n)$ denotes a [[Lucas numbers|Lucas number]]. |
==Proof== | ==Proof== | ||
Revision as of 00:23, 25 May 2017
Theorem
The following formula holds: $$L(n+1)L(n-1)-L(n)^2=5(-1)^{n+1},$$ where $L(n)$ denotes a Lucas number.
