Results 81 to 90 of about 321 (189)
On the Diophantine equation $\sum _{j=1}^kjF_j^p=F_n^q$ [PDF]
, 2018 summary:Let $F_n$ denote the $n^{th}$ term of the Fibonacci sequence. In this paper, we investigate the Diophantine equation $F_1^p+2F_2^p+\cdots +kF_{k}^p=F_{n}^q$ in the positive integers $k$ and $n$, where $p$ and $q$ are given positive integers.
Soydan, Gökhan +2 more
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Max–min of polynomials and exponential diophantine equations
Journal of Number Theory, 2010 In the first half of this paper, largely based on earlier work of \textit{R. Dvornicich, U. Zannier}, and the author [Acta Arith. 106, No. 2, 115--121 (2003; Zbl 1020.11018)], it is shown that for \(F \in {\mathbb Z}[x,y]\) one has \(\max_{x \in \mathbb Z \cap [-T,T]} \min_{y \in \mathbb Z} |F(x,y)| = o(T^{1/2})\) as \(T \to \infty\) if and only if ...
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The diophantine equation $\alpha^{x_1}_1\dots\alpha^{x_n}_n=f(x_1,\dots,x_n)$. II. [PDF]
, 2010 The paper solves a previously posed problem by proving a certain uniform bound for the number of solutions of certain polynomial-exponential diophantine ...
SCHMIDT W., CORVAJA P, ZANNIER, UMBERTO
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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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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 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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On prime powers in linear recurrence sequences. [PDF]
Ann Math Quebec, 2023 Odjoumani J, Ziegler V.
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On the exponential Diophantine equation \((m^2+1)^x+(cm^2-1)^y=(am)^z \) [PDF]
, 2014 Let \(m, a, c\) be positive integers with \(a≡3,5 (mod8)\). We show that when \(1+c=a^2\), the exponential Diophantine equation \((m^2+1)^x+(cm^2−1)^y=(am)^z\) has only the positive integer solution \((x,y,z)=(1,1,2)\) under the condition \(m≡±1 ...
Miyazaki, T., Terai, N.
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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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Counting Real Roots in Polynomial-Time via Diophantine Approximation. [PDF]
Found Comut Math, 2022 Rojas JM.
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