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
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