L(n)^2-5F(n)^2=4(-1)^n

Theorem

The following formula holds: $$L(n)^2-5F(n)^2=4(-1)^n,$$ where $L(n)$ denotes the $n$th Lucas number and $F(n)$ denotes the $n$th Fibonacci number.

References

• S.L. Basin and V.E. Hoggatt, Jr.: A Primer on the Fibonacci Sequence Part I (1963)... (previous)... (next)