Results 61 to 70 of about 1,519,699 (118)
An application of Frey's idea to exponential Diophantine equations
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1994 Let \(a\), \(b\), \(c\), \(l\), \(m\), \(n\) be relatively prime positive integers. In this paper it is shown that the equation \(la^ x+ mb^ y= nc^ z\), has a finite number of solutions in positive integers \(x\), \(y\), \(z\), all of which can be effectively determined. The effective procedure is based on: a) \textit{G.
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S-Unit Equations in Modules and Linear-Exponential Diophantine Equations
Proceedings of the 58th Annual ACM Symposium on Theory of ComputingLet $T$ be a positive integer, and $\mathcal{M}$ be a finitely presented module over the Laurent polynomial ring $\mathbb{Z}_{/T}[X_1^{\pm}, \ldots, X_N^{\pm}]$. We consider S-unit equations over $\mathcal{M}$: these are equations of the form $x_1 m_1 + \cdots + x_K m_K = m_0$, where the variables $x_1, \ldots, x_K$ range over the set of monomials ...
Ruiwen Dong, Doron Shafrir
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, 1988 Our purpose is to study a variety of Diophantine equations involving the Smarandache ...
Burton, Emil, Tutescu, Lucianu
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Curious Continued Fractions, Nonlinear Recurrences and Transcendental Numbers [PDF]
, 2015 We consider a family of integer sequences generated by nonlinear recurrences of the second order, which have the curious property that the terms of the sequence, and integer multiples of the ratios of successive terms (which are also integers), appear ...
Hone, Andrew N.W.
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Some exponential diophantine equations
Some exponential diophantine equations制度:新 ; 文部省報告番号:甲961号 ; 学位の種類:博士(理学) ; 授与年月日:1993-03-04 ; 早大学位記番号:新1907 ; 理工学図書館請求番号 ...
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A Complete Resolution of the Exponential Diophantine Equation
This paper determines all nonnegative integer solutions of the exponential Diophantine equation z^2=277665⋅17^6+34^n. After an elementary branch decomposition, the even-exponent branch is reduced to a finite factorization problem. The odd-exponent branch is transformed into the generalized Pell equation X^2−34Y^2=277665, subject to the additional ...
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DIOPHANTINE REPRESENTATION OF LEONARDO NUMBERS AND AN EXPONENTIAL DIOPHANTINE EQUATION
In this paper, we show that the positive Leonardo numbers are precisely the positive values of an explicitly constructed polynomial of degree nine in two variables, thereby providing an explicit Diophantine representation of the sequence. We also determine all nonnegative integer solutions of the exponential Diophantine equation L n = 2 a + 3 b + 5 c ,
Padmavathy, G, Subramani, Muthukrishnan
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Solution of the Exponential Diophantine Equation
Journal of Chemical, Biological and physical sciencesopenaire +1 more source