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- Fundamental_discriminant abstract "In mathematics, a fundamental discriminant D is an integer invariant in the theory of integral binary quadratic forms. If Q(x, y) = ax2 + bxy + cy2 is a quadratic form with integer coefficients, then D = b2 − 4ac is the discriminant of Q(x, y). Conversely, every integer D with D ≡ 0, 1 (mod 4) is the discriminant of some binary quadratic form with integer coefficients. Thus, all such integers are referred to as discriminants in this theory. Every discriminant may be written asD = D0f 2with D0 a discriminant and f a positive integer. A discriminant D is called a fundamental discriminant if f = 1 in every such decomposition. Conversely, every discriminant D ≠ 0 can be written uniquely as D0f 2 where D0 is a fundamental discriminant. Thus, fundamental discriminants play a similar role for discriminants as prime numbers do for all integers.There are explicit congruence conditions that give the set of fundamental discriminants. Specifically, D is a fundamental discriminant if, and only if, one of the following statements holds D ≡ 1 (mod 4) and is square-free, D = 4m, where m ≡ 2 or 3 (mod 4) and m is square-free.The first ten positive fundamental discriminants are: 1, 5, 8, 12, 13, 17, 21, 24, 28, 29, 33 (sequence A003658 in OEIS).The first ten negative fundamental discriminants are: −3, −4, −7, −8, −11, −15, −19, −20, −23, −24, −31 (sequence A003657 in OEIS).".
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- Fundamental_discriminant wikiPageRevisionID "567927755".
- Fundamental_discriminant wikiPageWikiLink 12_(number).
- Fundamental_discriminant wikiPageWikiLink 13_(number).
- Fundamental_discriminant wikiPageWikiLink 17_(number).
- Fundamental_discriminant wikiPageWikiLink 1_(number).
- Fundamental_discriminant wikiPageWikiLink 21_(number).
- Fundamental_discriminant wikiPageWikiLink 24_(number).
- Fundamental_discriminant wikiPageWikiLink 28_(number).
- Fundamental_discriminant wikiPageWikiLink 29_(number).
- Fundamental_discriminant wikiPageWikiLink 33_(number).
- Fundamental_discriminant wikiPageWikiLink 5_(number).
- Fundamental_discriminant wikiPageWikiLink 8_(number).
- Fundamental_discriminant wikiPageWikiLink Binary_function.
- Fundamental_discriminant wikiPageWikiLink Category:Algebraic_number_theory.
- Fundamental_discriminant wikiPageWikiLink Discriminant.
- Fundamental_discriminant wikiPageWikiLink Discriminant_of_an_algebraic_number_field.
- Fundamental_discriminant wikiPageWikiLink Fundamental_theorem_of_arithmetic.
- Fundamental_discriminant wikiPageWikiLink Greatest_common_divisor.
- Fundamental_discriminant wikiPageWikiLink Integer.
- Fundamental_discriminant wikiPageWikiLink Invariant_(mathematics).
- Fundamental_discriminant wikiPageWikiLink Isomorphism.
- Fundamental_discriminant wikiPageWikiLink Mathematics.
- Fundamental_discriminant wikiPageWikiLink Modular_arithmetic.
- Fundamental_discriminant wikiPageWikiLink Prime_number.
- Fundamental_discriminant wikiPageWikiLink Quadratic_field.
- Fundamental_discriminant wikiPageWikiLink Quadratic_form.
- Fundamental_discriminant wikiPageWikiLink Quadratic_integer.
- Fundamental_discriminant wikiPageWikiLink Rational_number.
- Fundamental_discriminant wikiPageWikiLink Springer_Science+Business_Media.
- Fundamental_discriminant wikiPageWikiLink Square-free_integer.
- Fundamental_discriminant wikiPageWikiLinkText "fundamental discriminant".
- Fundamental_discriminant wikiPageUsesTemplate Template:Cite_book.
- Fundamental_discriminant wikiPageUsesTemplate Template:OEIS.
- Fundamental_discriminant subject Category:Algebraic_number_theory.
- Fundamental_discriminant hypernym Invariant.
- Fundamental_discriminant comment "In mathematics, a fundamental discriminant D is an integer invariant in the theory of integral binary quadratic forms. If Q(x, y) = ax2 + bxy + cy2 is a quadratic form with integer coefficients, then D = b2 − 4ac is the discriminant of Q(x, y). Conversely, every integer D with D ≡ 0, 1 (mod 4) is the discriminant of some binary quadratic form with integer coefficients. Thus, all such integers are referred to as discriminants in this theory.".
- Fundamental_discriminant label "Fundamental discriminant".
- Fundamental_discriminant sameAs Q5508954.
- Fundamental_discriminant sameAs m.03cjlrb.
- Fundamental_discriminant sameAs Q5508954.
- Fundamental_discriminant wasDerivedFrom Fundamental_discriminant?oldid=567927755.
- Fundamental_discriminant isPrimaryTopicOf Fundamental_discriminant.