Results 101 to 110 of about 2,597 (231)
On the Diophantine equation x2+2k=yn
International Journal of Mathematics and Mathematical Sciences, 1997 By factorizing the equation x2+2k=yn, n≥3, k-even, in the field Q(i), various theorems regarding the solutions of this equation in rational integers are proved.
S. Akhtar Arif, Fadwa S. Abu Muriefah
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
Mathematika, Volume 72, Issue 2, April 2026.Abstract In 2019 Kleinbock and Wadleigh proved a “zero‐one law” for uniform inhomogeneous Diophantine approximations. We generalize this statement to arbitrary weight functions and establish a new and simple proof of this statement, based on the transference principle. We also give a complete description of the sets of g$g$‐Dirichlet pairs with a fixed
Vasiliy Neckrasov
wiley +1 more source
Computing all integer solutions of a genus 1 equation [PDF]
The Elliptic Logarithm Method has been applied with great successto the problem of computing all integer solutions of equations ofdegree 3 and 4 defining elliptic curves. We extend this methodto include any equation f(u,v)=0 that defines a curve of genus
Stroeker, R.J., Tzanakis, N.
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The diophantine equation $x^2+2^a\cdot 17^b=y^n$ [PDF]
, 2006 summary:Let $\mathbb {Z}$, $ \mathbb {N}$ be the sets of all integers and positive integers, respectively. Let $p$ be a fixed odd prime. Recently, there have been many papers concerned with solutions $(x, y, n, a, b)$ of the equation $ x^2+2^ap^b=y^n ...
Wang, Tingting, Mourad Abouzaid, Gou, Su
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On the Diophantine equation 2x + 11y = z2 [PDF]
Maejo International Journal of Science and Technology, 2013 In this paper it is shown that (3,0,3) is the only non-negative integer solution of the Diophantine equation 2x + 11y = z2.
Somchit Chotchaisthit
doaj
A remark on a Diophantine equation of S. S. Pillai [PDF]
summary:S. S. Pillai proved that for a fixed positive integer $a$, the exponential Diophantine equation $x^y-y^x= a$, $\min (x,y)>1$, has only finitely many solutions in integers $x$ and $y$.
Hoque, Azizul
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Diophantine Solutions Based Permutation for Image Encryption
Journal of Algorithms & Computational Technology, 2013 A permutation technique based on the resolution of the system of three independent Diophantine equations is presented. Each Diophantine equation parameters are two positive integers generated from a chaotic system.
J. S. Armand Eyebe Fouda +3 more
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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
One Diophantine Equation [PDF]
We solve a problem posed recently by J.H.E. Cohn, in proving that x = y = 1 is the only solution in nonnegative integers to the diophantine equation x^2 - 3 y^4 = -2.diophantine ...
Weger, B.M.M. de
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