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- ...teiner}} and into English by Abe Shenitzer as ''Diophantus and Diophantine Equations'' (Dolciani Mathematical Expositions 20, [[Mathematical Association of Amer ...loped theory of [[integer]] (rather than rational) solutions to polynomial equations, it is not included in this book.{{r|steiner}} ...6 Кб (846 слов) - 15:23, 27 февраля 2024
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- [[File:5-point Erdős-Diophantine graph.svg|thumb|A 5-node Erdős–Diophantine graph (node-distances as indicated).]] ...is an object in the [[mathematics|mathematical]] subject of [[Diophantine equations]] consisting of a set of [[integer]] points at integer distances in the pla ...4 Кб (485 слов) - 05:26, 4 марта 2024
- *[[Diophantine equation]] [[Category:Diophantine equations]] ...1 Кб (78 слов) - 11:06, 11 февраля 2024
- ...f any two is one less than a [[rational square]] is known as a '''rational diophantine {{mvar|m}}-tuple'''. == Diophantine ''m''-tuples == ...4 Кб (543 слова) - 15:23, 27 февраля 2024
- ...problem". His main area of research is [[number theory]], in particular [[Diophantine equation]]s, [[elliptic curve]]s, and applications of number theory in cryp ...contribution to number theory is in connection to [[Diophantine quintuple|Diophantine m-tuples]]. ...4 Кб (437 слов) - 11:44, 31 января 2024
- ...teiner}} and into English by Abe Shenitzer as ''Diophantus and Diophantine Equations'' (Dolciani Mathematical Expositions 20, [[Mathematical Association of Amer ...loped theory of [[integer]] (rather than rational) solutions to polynomial equations, it is not included in this book.{{r|steiner}} ...6 Кб (846 слов) - 15:23, 27 февраля 2024
- * solution of [[linear Diophantine system]]s, i.e. equation systems where the coefficient matrix and the right For the basic problem of solving a linear system of ''m'' equations in ''n'' variables, where <math>\scriptstyle m \,\leq\, n</math>, ABS metho ...5 Кб (618 слов) - 23:05, 26 декабря 2023
- In [[mathematics]], specifically the area of [[Diophantine approximation]], the '''Davenport–Schmidt theorem''' tells us how well a * [[Wolfgang M. Schmidt]]. ''Diophantine approximation''. Lecture Notes in Mathematics 785. Springer. (1980 [1996 wi ...3 Кб (356 слов) - 01:41, 25 февраля 2024
- ...s to study these equations.{{sfn|Hindry|Silverman|2000|loc=Preface|p=vii}} Diophantine geometry is part of the broader field of [[arithmetic geometry]]. Four [[theorem]]s in Diophantine geometry that are of fundamental importance include:{{sfn|Hindry|Silverman| ...9 Кб (1140 слов) - 15:23, 27 февраля 2024
- ...nian mathematician who specializes in [[number theory]] with emphasis on [[Diophantine equation]]s, [[recurrence relation|linear recurrences]] and the distributio * Diophantine Equations - Effective Methods for Diophantine Equations, 2009, [https://math.dartmouth.edu/archive/m105f12/public_html/lucaHungary1 ...4 Кб (454 слова) - 09:42, 8 марта 2024
- ...id=rNKGAwAAQBAJ&pg=PA21}}.</ref> These types are all the possible pairs of equations of the following seven forms:<ref>{{citation ...3 Кб (346 слов) - 02:10, 18 февраля 2024
- * ''Schmidt Wolfgang M.'' Diophantine approximation // Lecture Notes in Mathematics 785. Springer. (1980 [1996 wi * ''Schmidt Wolfgang M.'' Diophantine approximations and Diophantine equations // Lecture Notes in Mathematics, Springer Verlag 2000. ...5 Кб (143 слова) - 18:54, 19 сентября 2023
- {{Short description|Solution of some Diophantine equation}} In [[mathematics]], a [[Diophantine equation]] is an equation of the form ''P''(''x''<sub>1</sub>, ..., ''x''<s ...12 Кб (1617 слов) - 15:23, 27 февраля 2024
- ...по математике 785. Springer. (1980 [1996 год с небольшими исправлениями])/Diophantine approximation. Lecture Notes in Mathematics 785. Springer. (1980 [1996 with ...атематике, Springer Verlag 2000/Diophantine approximations and Diophantine equations, Lecture Notes in Mathematics, Springer Verlag 2000 ...6 Кб (160 слов) - 12:31, 1 октября 2023
- [[Category:Diophantine equations]] ...1 Кб (135 слов) - 06:21, 20 марта 2024
- ==Formulation as a Diophantine equation== [[Édouard Lucas]] formulated the cannonball problem as a [[Diophantine equation]] ...5 Кб (638 слов) - 16:36, 14 февраля 2024
- ...any variables.<ref>R. Brauer, ''A note on systems of homogeneous algebraic equations'', Bulletin of the American Mathematical Society, '''51''', pages 749-755 ( ...nk=Harold Davenport | title=Analytic methods for Diophantine equations and Diophantine inequalities | others=Edited and prepared by T. D. Browning. With a preface ...5 Кб (638 слов) - 13:44, 11 февраля 2024
- ...re is that the only non-trivial [[integer]] solutions of the [[exponential Diophantine equation]] ...re are only finitely many possible solutions <math>(x,y,m,n)</math> to the equations with [[prime number|prime]] divisors of <math>x</math> and <math>y</math> l ...6 Кб (776 слов) - 00:23, 16 марта 2024
- ...es, one for each [[unknown (mathematics)|unknown]], that satisfies all the equations or inequalities. ..., then there are no values of the unknowns that satisfy simultaneously all equations and inequalities. ...17 Кб (2541 слово) - 04:00, 4 марта 2024
- | title = On the Brocard–Ramanujan Diophantine equation {{math|''n''! + 1 {{=}} ''m''<sup>2</sup>}} | title = On the Diophantine equation {{math|''x''! + A {{=}} ''y''<sup>2</sup>}} ...6 Кб (776 слов) - 03:13, 12 февраля 2024
- ...[number theory]], encompassing areas such as [[analytic number theory]], [[diophantine equation]]s, and [[modular form]]s. ...2 Кб (156 слов) - 12:32, 26 марта 2024
