Results 31 to 40 of about 1,205,224 (205)
Application of the group action approach to solving linear Diophantine equations [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. ИнформатикаThe article substantiates a method for solving linear Diophantine equations using the theory of group actions. The purpose of this paper is to introduce actions of certain groups on the set of linear Diophantine equations and to study their ...
Chistov, Ivan Sergeevich +1 more
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On an diophantine equation [PDF]
Bulletin of the Australian Mathematical Society, 2000 In this note, we find all solutions of the diophatine equation x2 + 3m = yn, where (x, y, m, n) are non-negative integers with x ≠ 0 and n ≥ 3.
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On some Diophantine equations [PDF]
Journal of Inequalities and Applications, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sakarya Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü +3 more
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On the size of Diophantine m-tuples in imaginary quadratic number rings
Bulletin of Mathematical Sciences, 2021 A Diophantine m-tuple is a set of m distinct integers such that the product of any two distinct elements plus one is a perfect square. It was recently proven that there is no Diophantine quintuple in positive integers.
Nikola Adžaga
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Glasgow Mathematical Journal, 1985 I was recently challenged to find all the cases when the sum of three consecutive integral cubes is a square; that is to find all integral solutions x, y ofy2=(x−1)3+x3+(x+1)3=3x(x2+2)This is an example of a curve of genus 1. There is an effective procedure for finding all integral points on a given curve of genus 1 ([1, Theorem 4.2], [2]): that is, it
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Arrested development and fragmentation in strongly-interacting Floquet systems
SciPost Physics, 2023 We explore how interactions can facilitate classical like dynamics in models with sequentially activated hopping. Specifically, we add local and short range interaction terms to the Hamiltonian and ask for conditions ensuring the evolution acts as a ...
Matthew Wampler, Israel Klich
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The Solution of a Diophantine Equation [PDF]
Proceedings of the American Mathematical Society, 1952 in which we suppose that f(y) =f(yi, * ya) is a homogeneous polynomial, with integral coefficients, of degree m, where m is of the form 2P(2q+1), q being a non-negative integer, p is one of the integers 0, 1, * * *, n -1, and thus m 0 0 (mod 2n). We suppose further that the rank of the matrix of the forms Enl aajx (i= 1, , 2n) is 2n -1 and thus we may ...
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The Number of Partitions of a Set and Superelliptic Diophantine Equations [PDF]
, 2020 In this chapter we start by presenting some key results concerning the number of ordered k-partitions of multisets with equal sums. For these we give generating functions, recurrences and numerical examples.
Dorin Andrica +5 more
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Systems of Diophantine Equations [PDF]
Proceedings of the American Mathematical Society, 1951 where fi and gi are homogeneous polynomials with integral coefficients, fi being of degree n and gi being of degree m. If there are no integers s> 1, a k, 3' such that ak = sla , ij = s, where X, g are positive integers such that Xn =,m, then Xk= ak, yij=gi3 is defined to be a primitive solution of (1). If Xk=aQk, yij=fi3 is a primitive solution of (1),
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A CLASS OF DIOPHANTINE EQUATIONS [PDF]
Proceedings of the National Academy of Sciences, 1959 Nach Verf. hat \[ \alpha^x+\beta^x=\alpha^n+\beta^n,\quad \alpha,\beta=\tfrac 12 (1\pm\sqrt{-7}), \] für gegebene \(n\) höchstens zwei Lösungen und für \(n=2^m\) genau die triviale Lösung \(x=2^m\).
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