Results 11 to 20 of about 140 (135)

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
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An exponential diophantine equation [PDF]

Bulletin of the Australian Mathematical Society, 2001
Let p be an odd prime with p > 3. In this paper we give all positive integer solutions (x, y, m, n) of the equation x2 + p2m = yn, gcd (x, y) = 1, n > 2 satisfying 2 | n of 2 ∤ n and p ≢ (−1)(p−1)/2(mod 4n.
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Two exponential diophantine equations [PDF]

Journal de théorie des nombres de Bordeaux, 2017
The equation 3 a +5 b -7 c =1, to be solved in non-negative rational integers a,b,c, has been mentioned by Masser as an example for which there is still no algorithm to solve completely. Despite this, we find here all the solutions. The equation y 2 =3 a +2 b +1, to be solved in non-negative rational integers a,b and a rational integer y, has been ...
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The Exponential Diophantine Equation 4m2+1x+5m2-1y=(3m)z

Abstract and Applied Analysis, 2014
Let m be a positive integer. In this paper, using some properties of exponential diophantine equations and some results on the existence of primitive divisors of Lucas numbers, we prove that if m>90 and 3|m, then the equation 4m2+1x + 5m2-1y=(3m)z has ...
Juanli Su, Xiaoxue Li
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Small two-variable exponential Diophantine equations [PDF]

Mathematics of Computation, 1993
We examine exponential Diophantine equations of the form a b x = c d y + e a{b^x} = c{d^y} + e . Consider a ≤ 50 a \leq 50 , c ≤
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An upper bound for solutions of the Lebesgue-Nagell equation x 2 + a 2 = y n $x^{2}+a^{2}=y^{n}$

Journal of Inequalities and Applications, 2016
Let a be a positive integer with a > 1 $a>1$ , and let ( x , y , n ) $(x, y, n)$ be a positive integer solution of the equation x 2 + a 2 = y n $x^{2}+a^{2}=y^{n}$ , gcd ( x , y ) = 1 $\gcd(x, y)=1$ , n > 2 $n>2$ .
Xiaowei Pan
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Exponential diophantine equations in rings of positive characteristic [PDF]

Journal of Knot Theory and Its Ramifications, 2020
In this paper, we prove an algorithmical solvability of exponential-Diophantine equations in rings represented by matrices over fields of positive characteristic. Consider the system of exponential-Diophantine equations [Formula: see text] where [Formula: see text] are constants from matrix ring of characteristic [Formula: see text], [Formula: see ...
Chilikov, A. A., Belov-Kanel, Alexey
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A Survey on the ternary purely exponential diophantine equation ax + by = cz [PDF]

Surveys in Mathematics and its Applications, 2019
Let a, b, c be fixed coprime positive integers with min(a,b,c)>1. In this survey, we consider some unsolved problems and related works concerning the positive integer solutions (x,y,z) of the ternary purely exponential diophantine equation ax + by = cz.
Maohua Le, Reese Scott, Robert Styer
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Common values of two k-generalized Pell sequences [PDF]

Notes on Number Theory and Discrete Mathematics
Let k≥2 and let (Pₙ⁽ᵏ⁾)ₙ≥₂₋ₖ be the k-generalized Pell sequence defined by Pₙ⁽ᵏ⁾=2Pₙ₋₁⁽ᵏ⁾+2Pₙ₋₂⁽ᵏ⁾+...+2Pₙ₋ₖ⁽ᵏ⁾ for n≥2 with initial conditions P₋₍ₖ₋₂₎⁽ᵏ⁾=P₋₍ₖ₋₃₎⁽ᵏ⁾=...=P₋₁⁽ᵏ⁾=P₀⁽ᵏ⁾=0, and P₁⁽ᵏ⁾=1.
Zafer Şiar, Florian Luca, Faith Shadow Zottor   +2 more
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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
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