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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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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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Open Computer Science, 2018 We define a computable function f from positive integers to positive integers. We formulate a hypothesis which states that if a system S of equations of the forms xi· xj = xk and xi + 1 = xi has only finitely many solutions in non-negative integers x1, .
Tyszka Apoloniusz
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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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ON A DIOPHANTINE EQUATION OF CASSELS [PDF]
Glasgow Mathematical Journal, 2005 In 1985 J.W.S. Cassels solved the problem of determening all the triples of consecutive cubes whose sum is a square, \textit{i.e.} he solved completely the elliptic Diophantine equation \(\,y^2=3x(x^2+2)\) (the solutions for \(x\) are \(0\), \(1\), \(2\) and \(24\)).
Luca, F., Walsh, P. G.
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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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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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Diophantine Equation in Logarithms [PDF]
, 2023 The main work of these pages is written by myself under the supervisor of Dr. Omar Kihel, pertaining to continued fractions and applications , linear form in logarithms and the solutions of Diophantine equation Fn1 + Fn2 + Fn3 + Fn4 = 6a .
Tian, Zhao
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On the Diophantine equation $(2^x-1)(p^y-1)=2z^2$ [PDF]
, 2021 summary:Let $p$ be an odd prime. By using the elementary methods we prove that: (1) if $2\nmid x$, $p\equiv \pm 3\pmod 8,$ the Diophantine equation $(2^{x}-1)(p^{y}-1)=2z^{2}$ has no positive integer solution except when $p=3$ or $p$ is of the form $p ...
Tong, Ruizhou
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