Results 41 to 50 of about 1,430,683 (165)
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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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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AIChE Journal, EarlyView.Abstract Thermophilic anaerobic digestion (AD) is an attractive process due to its higher biogas yield compared to mesophilic digestion. To mitigate its higher heating demand and potential process instability, a dual‐layer control architecture comprising a decision‐making layer and an adaptive model predictive control (MPC) system is proposed.
Ali Moradvandi +3 more
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Three Diophantine equations concerning the polygonal numbers [PDF]
Notes on Number Theory and Discrete MathematicsMany authors investigated the problem about the linear combination of two polygonal numbers being a perfect square, i.e., the Diophantine equation mPₖ(x)+nPₖ(y)=z², where Pₖ(x) denotes the x-th k-polygonal number and m, n are positive integers.
Yong Zhang, Mei Jiang, Qiongzhi Tang
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Weighted veronese rings via convex semigroups
Bulletin of the London Mathematical Society, Volume 58, Issue 11, November 2026.Abstract We determine several properties of two‐dimensional normal affine semigroup rings, and in particular of weighted Veronese rings, including determinantal presentations, Gröbner bases, graded Hilbert series and graded Betti numbers, the structure of their associated graded rings, and their Koszul property.
Bek Chase +6 more
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On a Diophantine equation [PDF]
, 1998 summary:In this paper, we find all solutions of the Diophantine equation $x^2+2^\alpha 5^\beta 17^\gamma = y^n$ in positive integers $x,y\geq 1$, $\alpha ,\beta ,\gamma ,n\geq 3$ with $\gcd (x,y)=1$
Godinho, Hemar +6 more
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Tailoring Symmetry Breaking in Engineered van der Waals Superlattices
Advanced Materials, Volume 38, Issue 57, 13 October 2026.We pioneer a scheme to tailor superpotentials in graphene based on intrinsic substrate electronic orders rather than twist angle. The resulting superpotential folds graphene's Dirac cones to either Γ$\Gamma$ or K‐points, leading to distinct symmetry behaviors.
Keda Jin +7 more
wiley +1 more source
The diophantine equation x2+3m=yn
International Journal of Mathematics and Mathematical Sciences, 1998 The object ofthis paper is to prove the following.
S. Akhtar Arif, Fadwa S. Abu Muriefah
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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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