Diophantine equations in separated variables
نویسندگان
چکیده
منابع مشابه
Combinatorial Diophantine Equations and a Refinement of a Theorem on Separated Variables Equations
We look at Diophantine equations arising from equating classical counting functions such as perfect powers, binomial coefficients and Stirling numbers of the first and second kind. The proofs of the finiteness statements that we give use a variety of methods from modern number theory, such as effective and ineffective tools from Diophantine approximation. As a tool for one part of the statement...
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In this paper we find all solutions of four kinds of the Diophantine equations begin{equation*} ~x^{2}pm V_{t}xy-y^{2}pm x=0text{ and}~x^{2}pm V_{t}xy-y^{2}pm y=0, end{equation*}% for an odd number $t$, and, begin{equation*} ~x^{2}pm V_{t}xy+y^{2}-x=0text{ and}text{ }x^{2}pm V_{t}xy+y^{2}-y=0, end{equation*}% for an even number $t$, where $V_{n}$ is a generalized Lucas number. This pape...
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ژورنال
عنوان ژورنال: Periodica Mathematica Hungarica
سال: 2017
ISSN: 0031-5303,1588-2829
DOI: 10.1007/s10998-017-0195-y