Results 71 to 80 of about 321 (189)
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
wiley +1 more source
A p-adic Look at the Diophantine Equation x[sup 2]+11[sup 2k] = y[sup n] [PDF]
, 2009 Bu çalışma, 18-22 Eylül 2009 tarihleri arasında Rethymnon[Yunanistan]’da düzenlenen Exponential diophantine equationsprimitive divisors’da bildiri olarak sunulmuştur.We find all solutions of Diophantine equation x(2) + 11(2k) = y(n), x >= 1, y >= 1, k ...
Simos, T. E. +10 more
core +1 more source
A Diophantine equation involving one Linnik prime [PDF]
summary:Let $[\theta ]$ denote the integral part of the real number $\theta .$ We prove that for ...
Liu, Yuhui
core +1 more source
On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences. [PDF]
Ramanujan J, 2021 Ddamulira M, Luca F.
europepmc +1 more source
Exponential Diophantine equations [PDF]
Pacific Journal of Mathematics, 1982 Brenner, J. L., Foster, Lorraine L.
openaire +3 more sources
Complete solution of the exponential Diophantine equation \(P_n^x+P_{n+1}^x=P_m^y\) [PDF]
, 2022 In this paper, we find all the solutions of the title Diophantine equation in positive integer variables (m, n, x,y), where \(P_k\) is the kth term of the Pell ...
Togbe, Alain +4 more
core +1 more source
On the Diophantine equation $\frac{q^n-1}{q-1}=y$ [PDF]
, 2003 summary:There exist many results about the Diophantine equation $(q^n-1)/(q-1)=y^m$, where $m\ge 2$ and $n\geq 3$. In this paper, we suppose that $m=1$, $n$ is an odd integer and $q$ a power of a prime number.
Khosravi, Amir, Khosravi, Behrooz
core
On the exponential Diophantine equation ${\displaystyle p\cdot 3^{x}+p^{y}=z^2}$ with $p$ a prime number [PDF]
, 2023 In this paper we find non-negative integer solutions for exponential Diophantine equations of the type $p \cdot 3^x+ p^y=z^2,$ where $p$ is a prime number. We prove that such equation has a unique solution $\displaystyle{(x,y,z)=\left(\log_3(p-2), 0, p-1\
Ferreira, G. S. +2 more
core +1 more source
Solving exponential diophantine equations using lattice basis reduction algorithms [PDF]
, 1987 Let S be the set of all positive integers with prime divisors from a fixed finite set of primes. Algorithms are given for solving the diophantine inequality 0<x - y <yd in x, y ¿ S for fixed d ¿ (0, 1), and for the diophantine equation x + y = z in
Weger, de, B.M.M. +3 more
core +1 more source
Exponential diophantine equations with four terms
Indagationes Mathematicae, 1992 This article gives some examples how to make exponential diophantine equations more practical. The authors take the large exponential bounds for solutions given by Baker's method to computational available bounds. Let \(p\) and \(q\) be distinct primes less than 200. The main theorems are: (1) Every solution of the equation \(p^ x q^ y\pm p^ z \pm q^ w
Deze, Mo, Tijdeman, R.
openaire +2 more sources