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- Degen's_eight-square_identity abstract "In mathematics, Degen's eight-square identity establishes that the product of two numbers, each of which being a sum of eight squares, is itself the sum of eight squares.Namely:First discovered by Ferdinand Degen (Danish) around 1818, the identity was independently rediscovered by John Thomas Graves (1843) and Arthur Cayley (1845). The latter two derived it while working on an extension of quaternions called octonions. In algebraic terms the identity means that the norm of product of two octonions equals the product of their norms: . Similar statements are true for quaternions (Euler's four-square identity), complex numbers (the Brahmagupta–Fibonacci two-square identity) and real numbers. In 1898 Adolf Hurwitz proved that there is no similar bilinear identity for 16 squares (sedenions) or any other number of squares except for 1,2,4, and 8. However, in the 1960s, H. Zassenhaus, W. Eichhorn, and A. Pfister (independently) showed there can be a non-bilinear identity for 16 squares. Note that each quadrant reduces to a version of Euler's four-square identity:and similarly for the other three quadrants. By Pfister's theorem, a different sort of eight-square identity can be given where the are non-bilinear and merely rational functions of the . Thus,where,and,with,Incidentally, the obey the identity,".
- Degen's_eight-square_identity wikiPageExternalLink DegensEight-SquareIdentity.html.
- Degen's_eight-square_identity wikiPageExternalLink 0021c.
- Degen's_eight-square_identity wikiPageExternalLink ramanujan_page8.html&date=2009-10-25+23:07:36.
- Degen's_eight-square_identity wikiPageID "4982245".
- Degen's_eight-square_identity wikiPageRevisionID "595912060".
- Degen's_eight-square_identity hasPhotoCollection Degen's_eight-square_identity.
- Degen's_eight-square_identity subject Category:Analytic_number_theory.
- Degen's_eight-square_identity subject Category:Mathematical_identities.
- Degen's_eight-square_identity type Abstraction100002137.
- Degen's_eight-square_identity type Attribute100024264.
- Degen's_eight-square_identity type Identity104618070.
- Degen's_eight-square_identity type MathematicalIdentities.
- Degen's_eight-square_identity type Personality104617562.
- Degen's_eight-square_identity comment "In mathematics, Degen's eight-square identity establishes that the product of two numbers, each of which being a sum of eight squares, is itself the sum of eight squares.Namely:First discovered by Ferdinand Degen (Danish) around 1818, the identity was independently rediscovered by John Thomas Graves (1843) and Arthur Cayley (1845). The latter two derived it while working on an extension of quaternions called octonions.".
- Degen's_eight-square_identity label "Acht-kwadratenidentiteit van Degen".
- Degen's_eight-square_identity label "Degen's eight-square identity".
- Degen's_eight-square_identity label "Identità degli otto quadrati di Degen".
- Degen's_eight-square_identity label "Identité des huit carrés de Degen".
- Degen's_eight-square_identity label "Тождество восьми квадратов".
- Degen's_eight-square_identity sameAs Identité_des_huit_carrés_de_Degen.
- Degen's_eight-square_identity sameAs Identità_degli_otto_quadrati_di_Degen.
- Degen's_eight-square_identity sameAs 데겐의_여덟_제곱수_항등식.
- Degen's_eight-square_identity sameAs Acht-kwadratenidentiteit_van_Degen.
- Degen's_eight-square_identity sameAs m.0cyc69.
- Degen's_eight-square_identity sameAs Q1187196.
- Degen's_eight-square_identity sameAs Q1187196.
- Degen's_eight-square_identity sameAs Degen's_eight-square_identity.
- Degen's_eight-square_identity wasDerivedFrom Degen's_eight-square_identity?oldid=595912060.
- Degen's_eight-square_identity isPrimaryTopicOf Degen's_eight-square_identity.