Gelin-Cesàro Identity

Author

Eric W. Weisstein
March 6, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/Gelin-CesaroIdentity.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Gelin-CesaroIdentity.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Identity

((((Fibonacci[n])))^4)-(Fibonacci[n-2]) (Fibonacci[n-1]) (Fibonacci[n+1]) (Fibonacci[n+2])==1

FullSimplify[Fibonacci[n]^4-Fibonacci[n-2]Fibonacci[n-1]Fibonacci[n+1]Fibonacci[n+2]-1]

FullSimplify[%,n∈Integers]