Results 21 to 30 of about 1,519,699 (118)
The Diophantine Equation 8x+py=z2
The Scientific World Journal, 2015 Let p be a fixed odd prime. Using certain results of exponential Diophantine equations, we prove that (i) if p≡±3(mod 8), then the equation 8x+py=z2 has no positive integer solutions (x,y,z); (ii) if p≡7(mod 8), then the equation has only the solutions
Lan Qi, Xiaoxue Li
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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
doaj
Exponential diophantine equations in rings of positive characteristic [PDF]
Journal of Knot Theory and Its Ramifications, 2020 In this paper, we prove an algorithmical solvability of exponential-Diophantine equations in rings represented by matrices over fields of positive characteristic. Consider the system of exponential-Diophantine equations [Formula: see text] where [Formula: see text] are constants from matrix ring of characteristic [Formula: see text], [Formula: see ...
Chilikov, A. A., Belov-Kanel, Alexey
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On some exponential diophantine equations [PDF]
, 2019 Anadolu Üniversitesi ve Bilecik Şeyh Edebali Üniversitesi tarafından ortak yürütülen program.Üç bölümden oluşan bu çalışmada sayılar teorisinin insanlık tarihi kadar eski sayılabilecek problemlerinden birisi olan Diophantine denklemlerinin özel bir ...
Akkuş, Seda Nur
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On a conjecture on exponential Diophantine equations [PDF]
Acta Arithmetica, 2009 We study the solutions of a Diophantine equation of the form $a^x+b^y=c^z$, where $a\equiv 2 \pmod 4$, $b\equiv 3 \pmod 4$ and $\gcd (a,b,c)=1$. The main result is that if there exists a solution $(x,y,z)=(2,2,r)$ with $r>1$ odd then this is the only solution in integers greater than 1, with the possible exception of finitely many values $(c,r)$. We
Cipu, Mihai, Mignotte, Maurice
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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
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Communications on Pure and Applied Mathematics, Volume 79, Issue 9, Page 2107-2157, September 2026.ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone +3 more
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Exponential Diophantine equations [PDF]
, 2006 Kroz mnoštvo ilustrativnih primjera opisani su različiti pristupi za rješavanje eksponencijalnih diofantskih jednadžbi. Zadaci su prilagođeni učenicima srednje škole.Various approaches to solving exponential diophantine equations are described by a wide ...
Ilišević, I.
core
On 7‐adic Galois representations for elliptic curves over Q$\mathbb {Q}$
Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.Abstract In recent years, significant progress has been made on Mazur's Program B, with many authors beginning a systematic classification of all possible images of p$p$‐adic Galois representations attached to elliptic curves over Q$\mathbb {Q}$. Currently, the classification is only complete for p∈{2,3,13,17}$p \in \lbrace 2,3,13,17\rbrace$.
Lorenzo Furio, Davide Lombardo
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On the moments of exponential sums over r$r$‐free polynomials
Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.Abstract Let Fq[t]${\mathbb {F}}_q[t]$ denote the ring of polynomials over the finite field Fq${\mathbb {F}}_q$. Building off of techniques of Balog and Ruzsa and of Keil in the integer setting, we determine the precise order of magnitude of k$k$th moments of exponential sums over r$r$‐free polynomials in Fq[t]${\mathbb {F}}_q[t]$ for all k>0$k>0$.
Ben Doyle
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