Results 31 to 40 of about 446 (186)
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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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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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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S-Restricted Compositions Revisited [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 An S-restricted composition of a positive integer n is an ordered partition of n where each summand is drawn from a given subset S of positive integers. There are various problems regarding such compositions which have received attention in recent years.
Behrouz Zolfaghari +2 more
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Kripke on Gödel Incompleteness
Theoria, EarlyView.ABSTRACT This paper surveys six of Saul Kripke's highly creative ideas and results on Gödel incompleteness, from when he was an undergraduate to last publications. These include his extension of incompleteness from sentences to predicates, his model‐theoretic proof of incompleteness of arithmetic, his compelling analysis of incompleteness in terms of ...
Daniel Isaacson
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A number theoretic method for high order correlations of the Ulam map
四川大学学报. 自然科学版, 2020 In this paper, a number theoretic method is introduced to calculate the high order correlation functions of the Ulam map. In this method, the calculation is firstly transformed into solving a class of exponential Diophantine equations with variable ...
Zhou Xing-Wang
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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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Random Diophantine equations in the primes
Mathematika, Volume 72, Issue 3, July 2026.Abstract We consider equations of the form a1x1k+⋯+asxsk=0$a_{1}x_{1}^{k}+\cdots +a_{s}x_{s}^{k}=0$ where the variables xi$x_{i}$ are all taken to be primes. We define an analogue of the Hasse principle for solubility in the primes (which we call the prime Hasse principle), and prove that, whenever k⩾2$k\geqslant 2$, s⩾3k+2$s\geqslant 3k+2$, this holds
Philippa Holdridge
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Journal of MathematicsSolving the Diophantine equation has fascinated mathematicians from various civilizations. In this paper, we propose the resolution of quadratic Diophantine equations with integer coefficients.
Francklin Fenolahy +2 more
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