Exponential diophantine equations with four terms
Indagationes Mathematicae, 1992 This article gives some examples how to make exponential diophantine equations more practical. The authors take the large exponential bounds for solutions given by Baker's method to computational available bounds. Let \(p\) and \(q\) be distinct primes less than 200. The main theorems are: (1) Every solution of the equation \(p^ x q^ y\pm p^ z \pm q^ w
Deze, Mo, Tijdeman, R.
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On a variant of Pillai's problem involving <i>S</i>-units and Fibonacci numbers. [PDF]
Bol Soc Mat Mex, 2022 Ziegler V.
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Some exponential Diophantine equations III: A new look at the generalized Lebesgue–Nagell equation [PDF]
Let D be a fixed non-square integer, and let h(4D) denote the class number of binary quadratic primitive forms with discriminant 4D. Let k be a fixed even integer with gcd(D,k)=1.
Soydan, Gökhan, Le, Maohua
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On The Diophantine Equation:Jesmanowicz Conjecture And Selected Special Cases [PDF]
, 2020 In 1956, Jes´manowicz conjectured that for any primitive Pythagorean triple (a, b, c) with the Diophantine equation a2 + b2 = c2 and any positive integer k, the only solution of equation (ak)x +(bk)y = (ck)z, in positive integers, is (x, y, z) = (2, 2, 2)
Ahmed Balfaqih, Abdulrahman Hamed
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On the exponential Diophantine equation ${\displaystyle p\cdot 3^{x}+p^{y}=z^2}$ with $p$ a prime number [PDF]
, 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\
Ferreira, G. S. +2 more
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Mixing Rates of the Geometrical Neutral Lorenz Model. [PDF]
J Stat Phys, 2023 Bruin H, Canales Farías HH.
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On prime powers in linear recurrence sequences. [PDF]
Ann Math Quebec, 2023 Odjoumani J, Ziegler V.
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Counting Real Roots in Polynomial-Time via Diophantine Approximation. [PDF]
Found Comut Math, 2022 Rojas JM.
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Integers representable as differences of linear recurrence sequences. [PDF]
Res Number Theory, 2021 Tichy R, Vukusic I, Yang D, Ziegler V.
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Translation invariance, exponential sums, and Waring's problem [PDF]
, 2014 We describe mean value estimates for exponential sums of degree exceeding 2 that approach those conjectured to be best possible. The vehicle for this recent progress is the efficient congruencing method, which iteratively exploits the translation ...
Wooley, Trevor D. +2 more
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