Results 31 to 40 of about 20,685 (194)
On the cohomological equation for interval exchange maps [PDF]
, 2003 We exhibit an explicit full measure class of minimal interval exchange maps T for which the cohomological equation $\Psi -\Psi\circ T=\Phi$ has a bounded solution $\Psi$ provided that the datum $\Phi$ belongs to a finite codimension subspace of the space
Marmi, Stefano +2 more
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A note on the Diophantine equation (xᵏ-1)(yᵏ-1)²=zᵏ-1 [PDF]
Notes on Number Theory and Discrete MathematicsWe prove that, for k≥10, the Diophantine equation (xᵏ-1)(yᵏ-1)²=zᵏ-1 in positive integers x, y, z, k with z>1, has no solutions satisfying ...
Yangcheng Li
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A p-adic look at the Diophantine equation x^{2}+11^{2k}=y^{n} [PDF]
, 2009 We find all solutions of Diophantine equation x^{2}+11^{2k} = y^{n} where x>=1, y>=1, n>=3 and k is natural number.
Ch. Tsitouras +5 more
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Glasgow Mathematical Journal, 1985 I was recently challenged to find all the cases when the sum of three consecutive integral cubes is a square; that is to find all integral solutions x, y ofy2=(x−1)3+x3+(x+1)3=3x(x2+2)This is an example of a curve of genus 1. There is an effective procedure for finding all integral points on a given curve of genus 1 ([1, Theorem 4.2], [2]): that is, it
openaire +2 more sources
An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers [PDF]
, 2018 In this paper, we find all solutions of the exponential Diophantine equation $B_{n+1}^x-B_n^x=B_m$ in positive integer variables $(m, n, x)$, where $B_k$ is the $k$-th term of the Balancing sequence.Comment: Comments are ...
Faye, Bernadette +3 more
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Generating Pythagoras Quadruples in Symbolic 2-Plithogenic Commutative Rings [PDF]
Neutrosophic Sets and Systems, 2023 This paper is dedicated to find a general algorithm for generating different solutions for Pythagoras non-linear Diophantine equation .
Yaser Ahmad Alhasan +2 more
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On the Symbolic 2-plithogenic Fermat's Non-Linear Diophantine Equation [PDF]
Neutrosophic Sets and Systems, 2023 This paper is dedicated to find all symbolic 2-plithogenic integer solutions for the symbolic 2-plithogenic Fermat's Diophantine equation.
Heba Alrawashdeh +2 more
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A brief survey on the generalized Lebesgue-Ramanujan-Nagell equation [PDF]
Surveys in Mathematics and its Applications, 2020 The generalized Lebesgue-Ramanujan-Nagell equation is an important type of polynomial-exponential Diophantine equation in number theory. In this survey, the recent results and some unsolved problems of this equation are given.
Maohua Le, Gökhan Soydan
doaj
Journal of Inequalities and Applications, 2018 In this paper, we give a straightforward approach to obtaining the solution of the Diophantine equation 1w+1x+1y+1z=12 $\frac{1}{w} + \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{1}{2}$. We also establish that the Diophantine equation 1w+1x+1y+1z=mn $\
Tingting Bai
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A Method to Solve the Diophantine Equation $ax^2-by^2+c=0$
, 2006 It is a generalization of Pell's equation $x^2-Dy^2=0$. Here, we show that: if our Diophantine equation has a particular integer solution and $ab$ is not a perfect square, then the equation has an infinite number of solutions; in this case we find a ...
Smarandache, Florentin
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