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- Meyers_theorem abstract "In number theory, Meyer's theorem on quadratic forms states that an indefinite quadratic form Q in five or more variables over the field of rational numbers nontrivially represents zero. In other words, if the equationQ(x) = 0has a non-zero real solution, then it has a non-zero rational solution (the converse is obvious). By clearing the denominators, an integral solution x may also be found.Meyer's theorem is usually deduced from the Hasse–Minkowski theorem (which was proved later) and the following statement: A rational quadratic form in five or more variables represents zero over the field Qp of the p-adic numbers for all p.Meyer's theorem is best possible with respect to the number of variables: there are indefinite rational quadratic forms Q in four variables which do not represent zero. One family of examples is given by Q(x1,x2,x3,x4) = x12 + x22 − p(x32 + x42),where p is a prime number that is congruent to 3 modulo 4. This can be proved by the method of infinite descent using the fact that if the sum of two perfect squares is divisible by such a p then each summand is divisible by p.".
- Meyers_theorem wikiPageID "2115190".
- Meyers_theorem wikiPageLength "2677".
- Meyers_theorem wikiPageOutDegree "21".
- Meyers_theorem wikiPageRevisionID "565228258".
- Meyers_theorem wikiPageWikiLink Academic_Press.
- Meyers_theorem wikiPageWikiLink Category:Quadratic_forms.
- Meyers_theorem wikiPageWikiLink Category:Theorems_in_number_theory.
- Meyers_theorem wikiPageWikiLink Definite_quadratic_form.
- Meyers_theorem wikiPageWikiLink Ergebnisse_der_Mathematik_und_ihrer_Grenzgebiete.
- Meyers_theorem wikiPageWikiLink Field_(mathematics).
- Meyers_theorem wikiPageWikiLink Graduate_Texts_in_Mathematics.
- Meyers_theorem wikiPageWikiLink Hasse–Minkowski_theorem.
- Meyers_theorem wikiPageWikiLink Indefinite_quadratic_form.
- Meyers_theorem wikiPageWikiLink Infinite_descent.
- Meyers_theorem wikiPageWikiLink Lattice_(group).
- Meyers_theorem wikiPageWikiLink Modular_arithmetic.
- Meyers_theorem wikiPageWikiLink Number_theory.
- Meyers_theorem wikiPageWikiLink Oppenheim_conjecture.
- Meyers_theorem wikiPageWikiLink P-adic_number.
- Meyers_theorem wikiPageWikiLink Prime_number.
- Meyers_theorem wikiPageWikiLink Proof_by_infinite_descent.
- Meyers_theorem wikiPageWikiLink Quadratic_form.
- Meyers_theorem wikiPageWikiLink Rational_number.
- Meyers_theorem wikiPageWikiLink Real_number.
- Meyers_theorem wikiPageWikiLink Springer-Verlag.
- Meyers_theorem wikiPageWikiLink Springer_Science+Business_Media.
- Meyers_theorem wikiPageWikiLink Square_number.
- Meyers_theorem wikiPageWikiLinkText "Meyer's theorem".
- Meyers_theorem hasPhotoCollection Meyers_theorem.
- Meyers_theorem wikiPageUsesTemplate Template:Cite_book.
- Meyers_theorem wikiPageUsesTemplate Template:Cite_journal.
- Meyers_theorem wikiPageUsesTemplate Template:For.
- Meyers_theorem subject Category:Quadratic_forms.
- Meyers_theorem subject Category:Theorems_in_number_theory.
- Meyers_theorem comment "In number theory, Meyer's theorem on quadratic forms states that an indefinite quadratic form Q in five or more variables over the field of rational numbers nontrivially represents zero. In other words, if the equationQ(x) = 0has a non-zero real solution, then it has a non-zero rational solution (the converse is obvious).".
- Meyers_theorem label "Meyer's theorem".
- Meyers_theorem sameAs Théorème_de_Meyer.
- Meyers_theorem sameAs m.06n42b.
- Meyers_theorem sameAs Q6826396.
- Meyers_theorem sameAs Q6826396.
- Meyers_theorem wasDerivedFrom Meyers_theoremoldid=565228258.
- Meyers_theorem isPrimaryTopicOf Meyers_theorem.