Results 21 to 30 of about 446 (186)
Advances in Mechanical Engineering, 2023 Numerous real-world applications can be solved using the broadly adopted notions of intuitionistic fuzzy sets, Pythagorean fuzzy sets, and q-rung orthopair fuzzy sets.
Mudassir Shams +3 more
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On a Diophantine Equation [PDF]
Journal of the London Mathematical Society, 1951 Summary: Denote by \(N(a,b)\) the smallest integer \(n\) so that \[ \frac{a}{b}=\frac{1}{x_1}+\cdots+\frac{1}{x_n},\quad ...
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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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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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Diophantine equations involving factorials [PDF]
Mathematica Bohemica, 2017 We study the Diophantine equations $(k!)^n -k^n = (n!)^k-n^k$ and $(k!)^n +k^n = (n!)^k +n^k,$ where $k$ and $n$ are positive integers. We show that the first one holds if and only if $k=n$ or $(k,n)=(1,2),(2,1)$ and that the second one holds if and only
Horst Alzer, Florian Luca
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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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On simultaneous diophantine equations [PDF]
Acta Arithmetica, 2003 The authors investigate the number of solutions of the simultaneous Diophantine equations \[ x^2- (M^2+4)y^2= -4, \quad y^2-dz^2=1, \tag{1} \] where \(M\) is assumed to be an odd positive integer and where \(d\) is a squarefree integer. They show that for squarefree \(d\) with at most four distinct prime factors, system (1) can have at most one ...
Katayama, Shin-ichi, Levesque, Claude
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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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