Giacomo Candido devised his eponymous identity to prove that
\( {\displaystyle (F_{n}^{2}+F_{n+1}^{2}+F_{n+2}^{2})^{2} =2(F_{n}^{4}+F_{n+1}^{4}+F_{n+2}^{4})} \)
where \( F_{n} \)is the nth Fibonacci number.
The identity of Candido is that, for all real numbers x and y,[
\( {\displaystyle (x^{2}+y^{2}+(x+y)^{2})^{2} =2(x^{4}+y^{4}+(x+y)^{4})} \)
It is easy to prove that the identity holds in any commutative ring.
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License
