Results 31 to 40 of about 24,674 (246)
Diophantine non-integrability of a third order recurrence with the Laurent property [PDF]
, 2006 We consider a one-parameter family of third order nonlinear recurrence relations. Each member of this family satisfies the singularity confinement test, has a conserved quantity, and moreover has the Laurent property: all of the iterates are Laurent ...
Hone, Andrew N.W.
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On the classification of duality webs for graded quivers
Journal of High Energy Physics, 2020 We study the m-graded quiver theories associated to CY (m+2)-folds and their order (m + 1) dualities. We investigate how monodromies give rise to mutation invariants, which in turn can be formulated as Diophantine equations characterizing the space of ...
Sebastián Franco +2 more
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Diophantine equations related to quasicrystals: a note
, 2001 We give the general solution of three Diophantine equations in the ring of integer of the algebraic number field ${\bf Q}[{\sqr 5}]$. These equations are related to the problem of determination of the minimum distance in quasicrystals with fivefold ...
Pelantová, E., Perelomov, A. M.
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Random Diophantine equations, I
Advances in Mathematics, 2014 Comment: The results in this paper use an $L^2$-technique and supersede those in an earlier version (see arXiv:1110.3496) that relied on an $L^1$-argument, but for instructional purposes we found it useful to keep the older, technically simpler version.
Brüdern, Jörg, Dietmann, Rainer
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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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More Than 1700 Years of Word Equations
, 2015 Geometry and Diophantine equations have been ever-present in mathematics. Diophantus of Alexandria was born in the 3rd century (as far as we know), but a systematic mathematical study of word equations began only in the 20th century. So, the title of the
A Boudet +10 more
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On the Diophantine Equation x2 – kxy + ky2 + ly = 0, l = 2n
Annals of the West University of Timisoara: Mathematics and Computer Science, 2017 We consider the Diophantine equation x2-kxy+ky2+ ly = 0 for l = 2n and determine for which values of the odd integer k, it has a positive integer solution x and y.
Mavecha Sukrawan
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Recurrence relations for the number of solutions of a class of Diophantine equations [PDF]
, 2013 Recursive formulas are derived for the number of solutions of linear and quadratic Diophantine equations with positive coefficients. This result is further extended to general non-linear additive Diophantine equations. It is shown that all three types of
Krivoruchenko, M. I.
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Complete classification of discrete resonant Rossby/drift wave triads on periodic domains
, 2013 We consider the set of Diophantine equations that arise in the context of the barotropic vorticity equation on periodic domains, when nonlinear wave interactions are studied to leading order in the amplitudes.
Bustamante, Miguel D., Hayat, Umar
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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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