Results 21 to 30 of about 312 (173)
Padovan and Perrin numbers of the form 7ᵗ-5ᶻ-3ʸ-2ˣ [PDF]
Notes on Number Theory and Discrete MathematicsConsider the Padovan sequence (pₙ)ₙ≥₀ given by pₙ₊₃=pₙ₊₁+pₙ with p₀=p₁=p₂=1. Its companion sequence, the Perrin sequence (℘ₙ)ₙ≥₀, follows the same recursive formula as the Padovan numbers, but with different initial values: p₀=3, p₁=0 and p₂=2.
Djamel Bellaouar +2 more
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Exponential Diophantine equations for correlation functions of the Tchebyscheff maps
四川大学学报. 自然科学版, 2023 Tchebyscheff maps are typical chaotic maps. Correlation functions play a key role in the study of their statistical properties. This paper aims at the solutions of a class of exponential Diophantine equations arising in the calculation of correlation ...
ZHOU Xing-Wang
doaj
A Hasse-type principle for exponential Diophantine equations and its applications [PDF]
, 2016 We propose a conjecture, similar to Skolem's conjecture, on a Hasse-type principle for exponential Diophantine equations. We prove that in a sense the principle is valid for "almost all" equations.
Hajdu, Lajos, Bertók, Csanád
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Classical and modular approaches to exponential Diophantine equations - II. The Lebesgue-Nagell equation [PDF]
, 2006 This is the second in a series of papers where we combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based on some of the ideas of the proof of Fermat's Last ...
Mignotte, Maurice +2 more
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Exponential sums equations and tropical geometry [PDF]
, 2023 Zilber’s Exponential-Algebraic Closedness Conjecture states that algebraic varieties in Cn×(C×)n intersect the graph of complex exponentiation, unless that contradicts the algebraic and transcendence properties of exp.
Francesco Paolo Gallinaro +1 more
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Heights and multiplicative relations on algebraic varieties [PDF]
, 2007 Points on a subvariety X of a semi-abelian variety A that are contained in a subgroup, let the subgroup be of finite rank or algebraic, are subject to severe restrictions arithmetical nature. Finiteness results for intersections of X with subgroups of
Habegger, Philipp
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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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Diophantine equations after Fermat’s last theorem [PDF]
, 2009 The author considers the following two questions: {\parindent=7mm \item{(i)}Given a Diophantine equation, what information can be obtained by following the strategy of Wiles' proof of Fermat's last theorem?
Siksek, Samir, Samir Siksek
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A number theoretic method for high order correlations of the Ulam map
四川大学学报. 自然科学版, 2020 In this paper, a number theoretic method is introduced to calculate the high order correlation functions of the Ulam map. In this method, the calculation is firstly transformed into solving a class of exponential Diophantine equations with variable ...
Zhou Xing-Wang
doaj
On a conjecture on exponential Diophantine equations [PDF]
Acta Arithmetica, 2009 We study the solutions of a Diophantine equation of the form $a^x+b^y=c^z$, where $a\equiv 2 \pmod 4$, $b\equiv 3 \pmod 4$ and $\gcd (a,b,c)=1$. The main result is that if there exists a solution $(x,y,z)=(2,2,r)$ with $r>1$ odd then this is the only solution in integers greater than 1, with the possible exception of finitely many values $(c,r)$. We
Cipu, Mihai, Mignotte, Maurice
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