Morgado Identity
There are several results known as the Morgado identity. The first is
![F_nF_(n+1)F_(n+2)F_(n+4)F_(n+5)F_(n+6)+L_(n+3)^2=[F_(n+3)(2F_(n+2)F_(n+4)-F_(n+3)^2)]^2,](https://mathworld.wolfram.com/images/equations/MorgadoIdentity/NumberedEquation1.gif) |
(1)
|
where 
is a Fibonacci number and 
is a Lucas number (Morgado 1987, Dujella 1995).
A second Morgado identity is satisfied by generalized Fibonacci numbers 
,
 |
(2)
|
where
(Morgado 1987, Dujella 1996).
REFERENCES:
Dujella, A. "Diophantine Quadruples for Squares of Fibonacci and Lucas Numbers." Portugaliae Math. 52, 305-318, 1995.
Dujella, A. "Generalized Fibonacci Numbers and the Problem of Diophantus." Fib. Quart. 34, 164-175, 1996.
Morgado, J. "Note on Some Results of A. F. Horadam and A. G. Shannon Concerning a Catalan's Identity on Fibonacci Numbers." Portugaliae Math. 44, 243-252, 1987.
