Results 51 to 60 of about 446 (186)
Diophantine equations in semiprimes
Discrete Analysis, 2019 Diophantine equations in semiprimes, Discrete Analysis 2019:17, 21 pp. This paper considers the problem of finding integer solutions to integral polynomial equations of the form $$f(x_1,\dots,x_n)=0\qquad\qquad (*)$$ with the condition that each ...
Shuntaro Yamagishi
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Random Diophantine equations in the primes II
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract Let d⩾2$d\geqslant 2$ and n⩾d$n\geqslant d$ with (d,n)∉{(2,2),(3,3)}$(d,n)\notin \lbrace (2,2),(3,3)\rbrace$. We consider homogeneous Diophantine equations of degree d$d$ in n+1$n+1$ variables and whether they have solutions in the primes.
Philippa Holdridge
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Fortschritte der Physik, Volume 74, Issue 4, April 2026.ABSTRACT In this paper, we continue the development of the Cartan neural networks programme, launched with three previous publications, by focusing on some mathematical foundational aspects that we deem necessary for our next steps forward. The mathematical and conceptual results are diverse and span various mathematical fields, but the inspiring ...
Pietro Fré +4 more
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Diophantine equations and identities
International Journal of Mathematics and Mathematical Sciences, 1985 The general diophantine equations of the second and third degree are far from being totally solved. The equations considered in this paper are i) x2−my2=±1 ii) x3+my3+m2z3−3mxyz=1iii) Some fifth degree diopantine ...
Malvina Baica
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Integral geometry on discrete matrices
Moroccan Journal of Pure and Applied Analysis, 2021 In this note, we study the Radon transform and its dual on the discrete matrices by defining hyperplanes as being infinite sets of solutions of linear Diophantine equations. We then give an inversion formula and a support theorem.
Attioui Abdelbaki
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Separable Diophantine equations [PDF]
Transactions of the American Mathematical Society, 1945 Theoretically, as noted by Skolem [3, p. 21(1), the general problem of algebraic diophantine analysis is reducible to the case in which occur only equations and inequalities of degree not higher than the second. For the extensive class of separable systems defined in ?6, this reduction can be performed effectively, eventuating in the complete integer ...
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Solving the n $n$‐Player Tullock Contest
Journal of Public Economic Theory, Volume 28, Issue 2, April 2026.ABSTRACT The n $n$‐player Tullock contest with complete information is known to admit explicit solutions in special cases, such as (i) homogeneous valuations, (ii) constant returns, and (iii) two contestants. But can the model be solved more generally?
Christian Ewerhart
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GCD inequalities arising from codimension‐2 blowups
Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.Abstract Assuming a deep Diophantine geometry conjecture by Vojta, Silverman proved an inequality giving an upper bound for the greatest common divisor (GCD). In this paper, we unconditionally prove a weaker version of this inequality. The main ingredient is the Ru–Vojta theory, which provides an efficient method of using Schmidt subspace theorem.
Yu Yasufuku
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, 1967 Formulae are given furnishing all non-trivial integer solutions of the equation \[ (x^2-t^2)(y^2-t^2)=\biggl(\biggl({y-x\over 2}\biggr)^2-t^2\biggr)^2 \] considered for \(t=1\) by the reviewer and \textit{W. Sierpiński} [Elem. Math. 18, 132--133 (1963; Zbl 0126.07301)].
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A Repulsion Motif in Diophantine Equations [PDF]
The American Mathematical Monthly, 2011 Problems related to the existence of integral and rational points on cubic curves date back at least to Diophantus. A significant step in the modern theory of these equations was made by Siegel, who proved that a non-singular plane cubic equation has only finitely many integral solutions.
Everest, G, Ward, T
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