Results 11 to 20 of about 7,736 (165)
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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Two exponential Diophantine equations [PDF]
Glasgow Mathematical Journal, 1997 In [3], two open problems were whether either of the diophantine equationswith n ∈ Z and f a prime number, is solvable if ω > 3 and 3 √ ω, but in this paper we allow f to be any (rational) integer and also 3 | ω. Equations of this form and more general ones can effectively be solved [5] with an advanced method based on analytical results, but the ...
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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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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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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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New connection formulae for some q-orthogonal polynomials in q-Askey scheme [PDF]
, 2007 New nonlinear connection formulae of the q-orthogonal polynomials, such continuous q-Laguerre, continuous big q-Hermite, q-Meixner-Pollaczek and q-Gegenbauer polynomials, in terms of their respective classical analogues are obtained using a special ...
A Yanallah +7 more
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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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, 2007 We introduce a new class of deterministic networks by associating networks with Diophantine equations, thus relating network topology to algebraic properties. The network is formed by rep- resenting integers as vertices and by drawing cliques between M
Bedogne, C, Masucci, AP, Rodgers, GJ
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Hilbert's 10th Problem for solutions in a subring of Q [PDF]
, 2019 Yuri Matiyasevich's theorem states that the set of all Diophantine equations which have a solution in non-negative integers is not recursive. Craig Smoryński's theorem states that the set of all Diophantine equations which have at most finitely many ...
Peszek, Agnieszka, Tyszka, Apoloniusz
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