Results 241 to 250 of about 190,474 (279)

Class Numbers of Indefinite Binary Quadratic Forms

Journal of Mathematical Sciences, 2003
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Factoring with Binary Quadratic Forms

1989
In the opening paragraphs of Article 329 of the Disquisitiones, Gauss, a master at calculating, writes [pp. 396–397], The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic ...
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Representation of Binary Quadratic Forms by a Quaternary Form

Journal of Mathematical Sciences, 2005
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Binary Quadratic Forms

2007
Johannes Buchmann, Ulrich Vollmer
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Positive Definite Binary Quadratic Forms

2007
Abstract A significant portion of Gauss’s Disquitiones Arithmeticae is about binary quadratic forms. Since then there have been numerous treatments, especially for the positive definite case. The most relevant reference for us will be Cox’s book [26]. Also many of the routines described here have built-in versions in PARI.
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On indefinite binary quadratic forms and quadratic ideals

2008
The author proves several results characterizing indefinite binary quadratic forms of the type \(F_i=(k-i^2,2i,-1)\), \(1\leq i\leq m\) where \(m=\lfloor\sqrt k\rfloor\). The results of the paper include: (1) an existence result for quadratic forms of this type, (2) a simple characterization of the reduction number of the quadratic form \(F_i\) where \(
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INDEFINITE BINARY QUADRATIC FORMS

The Quarterly Journal of Mathematics, 1950
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A Convex Reformulation and an Outer Approximation for a Large Class of Binary Quadratic Programs

Operations Research, 2023
Borzou Rostami, Fausto Errico, Andrea Lodi   +2 more
exaly  

Arithmetic Progressions Represented by Binary Quadratic Forms

Summary: Given an arbitrary irreducible integral binary quadratic form, we show how to construct, in parametric terms, arithmetic progressions of nine terms all of which can be represented by the given binary quadratic form. For certain binary quadratic forms, we can extend the length of the arithmetic progressions to 11 terms.
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Closed-form formulas for evaluating r-flip moves to the unconstrained binary quadratic programming problem

Computers and Operations Research, 2020
Eduardo Anacleto, Cláudio Meneses, Santiago Ravelo   +2 more
exaly