# Catalan’s identity

Let ${f}_{n}$ be the *n*th Fibonacci number^{} $n>1$, then the following identity is called *Catalan’s identity*.

$${f}_{n}^{2}-{f}_{n+r}{f}_{n-r}={(-1)}^{n-r}{f}_{r}^{2}.$$ |

For $r=1$ we have Cassini’s identity.

Title | Catalan’s identity |
---|---|

Canonical name | CatalansIdentity |

Date of creation | 2013-03-22 14:42:56 |

Last modified on | 2013-03-22 14:42:56 |

Owner | vmoraru (1243) |

Last modified by | vmoraru (1243) |

Numerical id | 7 |

Author | vmoraru (1243) |

Entry type | Theorem |

Classification | msc 11B39 |

Related topic | ProofofCassinisIdentity |