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- Meyer's_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.".
- Meyer's_theorem wikiPageID "2115190".
- Meyer's_theorem wikiPageRevisionID "565228258".
- Meyer's_theorem hasPhotoCollection Meyer's_theorem.
- Meyer's_theorem subject Category:Quadratic_forms.
- Meyer's_theorem subject Category:Theorems_in_number_theory.
- Meyer's_theorem type Abstraction100002137.
- Meyer's_theorem type Communication100033020.
- Meyer's_theorem type Form106290637.
- Meyer's_theorem type LanguageUnit106284225.
- Meyer's_theorem type Message106598915.
- Meyer's_theorem type Part113809207.
- Meyer's_theorem type Proposition106750804.
- Meyer's_theorem type QuadraticForms.
- Meyer's_theorem type Relation100031921.
- Meyer's_theorem type Statement106722453.
- Meyer's_theorem type Theorem106752293.
- Meyer's_theorem type TheoremsInNumberTheory.
- Meyer's_theorem type Word106286395.
- Meyer's_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).".
- Meyer's_theorem label "Meyer's theorem".
- Meyer's_theorem label "Théorème de Meyer".
- Meyer's_theorem sameAs Théorème_de_Meyer.
- Meyer's_theorem sameAs m.06n42b.
- Meyer's_theorem sameAs Q6826396.
- Meyer's_theorem sameAs Q6826396.
- Meyer's_theorem sameAs Meyer's_theorem.
- Meyer's_theorem wasDerivedFrom Meyer's_theorem?oldid=565228258.
- Meyer's_theorem isPrimaryTopicOf Meyer's_theorem.