There are two identities known as Catalan's identity.
The first is
 |
where 
is a Fibonacci number. Letting 
gives Cassini's Identity.
The second is the trivariate identity on partition of cubes into a sum of three squares given by
![(x^2+y^2+z^2)^3=[x(=3z^2-x^2-y^2)]^2+[y(3z^2-x^2-y^2)]^2
+[z(z^2-3x^2-3y^2)]^2.](/images/equations/CatalansIdentity/NumberedEquation2.svg) |
Catalan's Identity
See also
Cassini's Identity, d'Ocagne's Identity, Fibonacci NumberExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Catalan's Identity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CatalansIdentity.html