Results 21 to 30 of about 92,931 (194)
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
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On the Exponential Diophantine Equation p.3x + p y = z 2 with p a Prime Number [PDF]
Annals of Pure and Applied Mathematics, 2023 In this paper we find non-negative integer solutions for exponential Diophantine equations of the type $p \cdot 3^x+ p^y=z^2,$ where $p$ is a prime number. We prove that such equation has a unique solution $\displaystyle{(x,y,z)=\left(\log_3(p-2), 0, p-1\
Anderson Porto +2 more
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On the exponential Diophantine equation $x^2+p^mq^n=2y^p$ [PDF]
New Zealand Journal of Mathematics, 2023 We study the exponential Diophantine equation $x^2+p^mq^n=2y^p$ in positive integers $x,y,m,n$, and odd primes $p$ and $q$ using primitive divisors of Lehmer sequences in combination with elementary number theory.
K. Chakraborty, Azizul Hoque
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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]
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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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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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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On the Exponential Diophantine Equation 29^x- 3^y = z^2
International Journal of Latest Technology in Engineering, Management & Applied Science, 2023 Let x,y and z be non-negative integers. We prove that the exponential Diophantine equation 29x- 3y = z2 has the unique solution (x,y,z) = (0,0,0).
T. Kaewong, W. Chuayjan, S. Thongnak
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Two exponential diophantine equations [PDF]
Journal de théorie des nombres de Bordeaux, 2017 The equation 3 a + 5 b -
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More on the Exponential Diophantine Equation 23x + 233y = z2
Annals of Pure and Applied Mathematics, 2023 . In this paper, it is shown that the exponential diophantine equation 23 (cid:3) (cid:4) 233 (cid:5) (cid:6) (cid:7) (cid:8) is found to have a unique solution (cid:9)x, y, z(cid:14) (cid:6) (cid:9)1, 1, 16(cid:14) in non-negative integers x, y, and z ...
Gnanendra Rao Chikkavarapu
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