Results 91 to 100 of about 1,000 (210)

Pythagorean triangles of equal areas

International Journal of Mathematics and Mathematical Sciences, 1988
The main intent in this paper is to find triples of Rational Pythagorean Triangles (abbr. RPT) having equal areas. A new method of solving a2+ab+b2=c2 is to set a=y−1, b=y+1, y∈N−{0,1} and get Pell's equation c2−3y2=1. To solve a2−ab−b2=c2, we set a=12(y+
Malvina Baica
doaj   +1 more source

On Dirichlet problem for string equation, Poncelet problem, Pell-Abel equation, and some other related problems [PDF]

, 2006
У плоскій області, що обмежена біквадратною кривою, розглядається проблема єдиності розв'язку задачі Діріхле для рівняння коливання струни. Показано, що ця проблема еквівалентна класичній проблемі Понселе з проективної геометрії для двох придатних ...
Жеданов, А.С., Бурский, В.П.   +1 more
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Beyond Expansion IV: Traces of Thin Semigroups

Discrete Analysis, 2018
Beyond Expansion IV: Traces of Thin Semigroups, Discrete Analysis 2018:6, 27 pp. This is the fourth in a series of papers by Bourgain and Kontorovich that study the arithmetic properties of groups and semigroups of 2-by-2 integer matrices.
Jean Bourgain, Alex Kontorovich
doaj   +1 more source

Rational Polynomial Pell Equations. [PDF]

, 2013
Let R denote either the integers or the rationals and let d(x) be a square-free polynomial in R[x]. In this thesis we study the question of when does the polynomial Pell equation, f(x)^2-d(x)g(x)^2=1 have solutions f(x), g(x) in R[x] with g(x) non-zero.
Scherr, Zachary L.
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Powers in the Lucas sequence when the index is divisible by three [PDF]

, 2011
In this paper the m-powers with m ≥ 2 included in the Lucas sequences when the index satisfies some conditions are ...
Rodrigo Hitos, Javier, López González, M. Dolores   +1 more
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Extremal fixed points and Diophantine equations

Journal of High Energy Physics
The coupling constants of fixed points in the ϵ expansion at one loop are known to satisfy a quadratic bound due to Rychkov and Stergiou. We refer to fixed points that saturate this bound as extremal fixed points.
Christopher P. Herzog, Christian B. Jepsen, Hugh Osborn, Yaron Oz   +3 more
doaj   +1 more source

Hyperbolic reflections on pell's equation

Journal of Number Theory, 1989
It was conjectured by \textit{N. C. Ankeny}, \textit{E. Artin} and \textit{S. Chowla} [Ann. Math., II. Ser. 56, 479-493 (1952; Zbl 0049.306)] that the fundamental solution \((x_ 0,y_ 0)\) to the Pellian equation \(x^ 2- py^ 2=-1\) (p a prime congruent to 1 modulo 4) satisfies p \(\nmid y_ 0\). In an attempt to understand the nature of this problem, the
openaire   +1 more source

Positive integer solutions of some pell equations [PDF]

, 2014
Let d be a positive integer which is not a perfect square. In this paper, by using continued fraction expansion of ?d, we find fundamental solution of some Pell equation.
Nurul Nadiah Zainal Abidin
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Zagier’s reduction theory for indefinite binary quadratic forms and the Fermat-Pell Equation [PDF]

, 2020
We give an in depth description of indefinite binary quadratic forms with a particular emphasis on Zagier’s reduction theory for such forms. We also connect this theory with the theory of minus continued fractions and as a further application we offer a ...
Steward, Stephen Michael, NC DOCKS at The University of North Carolina at Greensboro   +1 more
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Pell denklemleri [PDF]

, 2012
06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması ...
Güney, Merve
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