Results 71 to 80 of about 2,595 (231)
A note on the ternary Diophantine equation x2 − y2m = zn
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 Let ℕ be the set of all positive integers. In this paper, using some known results on various types of Diophantine equations, we solve a couple of special cases of the ternary equation x2 − y2m = zn, x, y, z, m, n ∈ ℕ, gcd(x, y) = 1, m ≥ 2, n ≥ 3.
Bérczes Attila +3 more
doaj +1 more source
, 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)].
openaire +2 more sources
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
openaire +5 more sources
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
wiley +1 more source
Integral zeroes of Krawtchouk polynomials [PDF]
, 2012 This thesis was submitted for the degree of Master of Philosophy and awarded by Brunel University.Krawtchouk polynomials appear in many various areas of mathematics starting from discrete mathematics (e.g., in coding theory), association schemes, and in ...
Alenezi, Ahmad M
core
ON SOLVING A QUADRATIC DIOPHANTINE EQUATION
, 2022 Diophantine Equations named after ancient Greek mathematician Diophantus, plays a vital role not only in number theory but also in several branches of science.
Dr. R. Sivaraman
core +1 more source
On the Diophantine equation x2+p2k+1=4yn
International Journal of Mathematics and Mathematical Sciences, 2002 It has been proved that if p is an odd prime, y>1, k≥0, n is an integer greater than or equal to 4, (n,3h)=1 where h is the class number of the field Q(−p), then the equation x2+p2k+1=4yn has exactly five families of solution in the positive integers x ...
S. Akhtar Arif, Amal S. Al-Ali
doaj +1 more source
Some bounds related to the 2‐adic Littlewood conjecture
Mathematika, Volume 72, Issue 2, April 2026.Abstract For every irrational real α$\alpha$, let M(α)=supn⩾1an(α)$M(\alpha) = \sup _{n\geqslant 1} a_n(\alpha)$ denote the largest partial quotient in its continued fraction expansion (or ∞$\infty$, if unbounded). The 2‐adic Littlewood conjecture (2LC) can be stated as follows: There exists no irrational α$\alpha$ such that M(2kα)$M(2^k \alpha)$ is ...
Dinis Vitorino, Ingrid Vukusic
wiley +1 more source
On a quartic diophantine equation
, 1996 In this paper we consider the quartic diophantine equation 3(y2 – 1) = 2x2(x2 – 1) in integers x and y. We show that this equation does not have any other solutions (x, y) with x¿0 than those given by x = 0,1,2,3,6,91.
Weger, de, B.M.M. +3 more
core +1 more source
On Some Methods for Solution of Linear Diophantine Equations
Universal Journal of Mathematics and Applications, 2020 The paper considers a linear Diophantine equation. A method (algorithm) for finding a general class of solutions of equation is proposed. The proposed algorithm is explained by examples of equations with two and three variables, trying to direct the ...
Azam Imomov, Yorqin T. Khodjaev
doaj +1 more source