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Mathematical identities for the Fibonacci numbers
Cassini's identity (sometimes called Simson's identity), Catalan's identity and Vajda's identity are mathematical identities for the Fibonacci numbers
Cassini and Catalan identities
Cassini_and_Catalan_identities
two-square identity Candido's identity Cassini and Catalan identities Degen's eight-square identity Difference of two squares Euler's four-square identity Euler's
List of mathematical identities
List_of_mathematical_identities
Numbers obtained by adding the two previous ones
them: Cassini's identity states that F n 2 − F n + 1 F n − 1 = ( − 1 ) n − 1 {\displaystyle F_{n}^{2}-F_{n+1}F_{n-1}=(-1)^{n-1}} Catalan's identity is a
Fibonacci_sequence
Topics referred to by the same term
multiplication the Cassini and Catalan identities on Fibonacci numbers This disambiguation page lists articles associated with the title Fibonacci's identity. If an
Fibonacci's_identity
List of terms created from a person's name
astronomer and mathematician – Cassini Division, Cassini oval, Cassini's laws, Cassini and Catalan identities, Cassini's moon maiden (a pareidolia in Promontorium
List_of_eponyms_(A–K)
Historical French state (855–1487)
myth of Provence: identity and territory of a region (16th–20th century)] (in French). Éditions Ellipses. Carte de Cassini [Cassini map] (in French).
County_of_Provence
Infinite integer series where the next number is the sum of the two preceding it
<3L_{n}^{-5}.} Many of the Fibonacci identities have parallels in Lucas numbers. For example, the Cassini identity becomes L n 2 − L n − 1 L n + 1 = (
Lucas_number
Symbolic depiction of spatial relationships
of a sense of national identity". During World War I (WWI), cameras were mounted in airplanes that flew over battlefields and took photographs that were
Map
as a model with the Eileen Ford agency. Igor and Oleg Cassini, born Igor Cassini Loiewski and Oleg Cassini Loiewski, respectively. Igor, the younger brother
List of people who adopted matrilineal surnames
List_of_people_who_adopted_matrilineal_surnames
One hundred years, from 2001 to 2100
Jupiter and Saturn. At Jupiter, the Galileo orbiter was retired in 2003 and replaced with a second scientific orbiter in 2016. At Saturn, Cassini–Huygens
21st_century
flight projects including Galileo, Cassini, Mars Pathfinder, Mars Exploration Rovers Joseph Strauss – structural engineer and designer, chief engineer of the
List_of_German_Americans
Capital and largest city of France
Retrieved 24 April 2025. Darbyshire, Drew (8 April 2025). "Wigan Warriors and Catalans Dragons progress Paris plans for 2026". Wigan Today. Retrieved 15 May
Paris
Evolution of the art and science of mapmaking
Domenico Cassini, who perfected a method of determining longitude by the observation of movement of Jupiter's satellites. Cassini, along with the aid and support
History_of_cartography
American citizens of Italian descent
important role in American, Italian, European, Pan-American and Western histories and national identities. This emphasis on identification with a specific historical
Italian_Americans
Herring, S. W.; Cassini, G. H.; Tarquini, J.; Kuznetsov, A. (2023). "Myology of the masticatory apparatus of herbivorous mammals and a novel classification
2023_in_paleomammalogy
Region of France
languages and dialects made provision for Breton, Basque, Catalan and old Provençal but not for Corsican, Dutch (West Flemish) or Alsatian in Alsace and Moselle
Alsace
Subprefecture and commune in Occitania, France
the Catalan lords (Bellonids) at this intrusion of Frankish power over the lands of Gothia. For suppressing Berenguer of Toulouse and the Catalans, Louis
Narbonne
Number used to approximate the square root of 2
} Many identities can be derived or proven from these definitions; for instance an identity analogous to Cassini's identity for Fibonacci numbers
Pell_number
Commune in Pays de la Loire, France
works of Art & Language for 5 years]. CCMA (in Catalan). 324cat. Retrieved 19 October 2018. "Art and language uncompleted – Philippe Méaille collection
Montsoreau
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