Results 61 to 70 of about 312 (173)
Diophantine tuples and product sets in shifted powers
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract Let k⩾2$k\geqslant 2$ and n≠0$n\ne 0$. A Diophantine tuple with property Dk(n)$D_k(n)$ is a set of positive integers A$A$ such that ab+n$ab+n$ is a k$k$th power for all a,b∈A$a,b\in A$ with a≠b$a\ne b$. Such generalizations of classical Diophantine tuples have been studied extensively.
Ernie Croot, Chi Hoi Yip
wiley +1 more source
A note on the exponential Diophantine equation \((A^2n)^x+(B^2n)^y=((A^2+B^2)n)^z\) [PDF]
, 2020 Let \(A\) $B$ be positive integers such that $\min\{A,B\}>1$, $\gcd(A,B) = 1$ and $2|B.$ In this paper, using an upper bound for solutions of ternary purely exponential Diophantine equations due to R. Scott and R.
Maohua Le +3 more
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A universal example for quantitative semi‐uniform stability
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract We characterise quantitative semi‐uniform stability for C0$C_0$‐semigroups arising from port‐Hamiltonian systems, complementing recent works on exponential and strong stability. With the result, we present a simple universal example class of port‐Hamiltonian C0$C_0$‐semigroups exhibiting arbitrary decay rates slower than t−1/2$t^{-1/2}$.
Sahiba Arora +3 more
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Elementary methods for solving some diophantine equations and their applications [PDF]
, 2015 Diophantine denklemleri katsayıları tamsayılar olan iki yada daha fazla değişkenli denklemlerdir. Genel olarak bu denklemleri Lineer ve Üstel Diophantine Denklemleri olarak iki farklı şekilde sınıflandırabiliriz.
Ağaoğlu, Caner
core
Plank theorems and their applications: A survey
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract Plank problems concern the covering of convex bodies by planks in Euclidean space and are related to famous open problems in convex geometry. In this survey, we introduce plank problems and present surprising applications of plank theorems in various areas of mathematics.
William Verreault
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The Davenport–Heilbronn method: 80 years on
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract The Davenport–Heilbronn method is a version of the circle method that was developed for studying Diophantine inequalities in the paper (Davenport and Heilbronn, J. Lond. Math. Soc. (1) 21 (1946), 185–193). We discuss the main ideas in the paper, together with an account of the development of the subject in the intervening 80 years.
Tim Browning
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Diophantine equations in positive characteristic [PDF]
, 2019 In this thesis three different topics in number theory are studied. The first part deals with exponential Diophantine equations in positive characteristic. In the second part various statistical properties of class groups are proven.
Koymans, P.H.
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The dimension of well approximable numbers
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract In this survey article, we explore a central theme in Diophantine approximation inspired by a celebrated result of Besicovitch on the Hausdorff dimension of well approximable real numbers. We outline some of the key developments stemming from Besicovitch's result, with a focus on the mass transference principle, ubiquity and Diophantine ...
Victor Beresnevich, Sanju Velani
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Exponential Diophantine equations [PDF]
Pacific Journal of Mathematics, 1982 Brenner, J. L., Foster, Lorraine L.
openaire +3 more sources
On the Exponential Diophantine Equation 7^x − 5^y = z^2 [PDF]
In this paper, we address the exponential Diophantine equation 7x − 5y = z2 , seeking non-negative integer solutions for x, y, and z. Using many congruence theorems and Catalan’s conjecture, we prove the existence of a single solution. Our analysis shows
BUDEE U ZAMAN
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