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Fibonacci and Lucas numbers of the form -2^a-3^b-5^c+7^d
Revista IntegraciónIn this note we find all Fibonacci and Lucas numbers of the form -2^a-3^b-5^c+7^d where a, b, c, d are non-negative integers, with 0 ≤ max{a, b, c} ≤ d. This result gives an answer to a question posed by Qu, Zeng and Cao.
Sofía Ibarra +1 more
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Hypergeometric transformations of linear forms in one logarithm
Functiones et Approximatio Commentarii Mathematici, 2008 We discuss hypergeometric constructions of rational approximations to values of the logarithm function.
Viola, Carlo, Zudilin, Wadim
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Linear forms in elliptic logarithms
Journal of Number Theory, 1985 The author studies lower bounds for linear forms in elliptic integrals in the case of complex multiplications, and related estimates for dependence relations of such numbers. His results considerably improves on the previous works of D. Masser and M. Anderson on these topics, the main feature being a sharp dependence on the heights of the corresponding
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Linear forms in the logarithms of three positive rational numbers [PDF]
Journal de théorie des nombres de Bordeaux, 1997 In this paper we prove a lower bound for the linear dependence of three positive rational numbers under certain weak linear independence conditions on the coefficients of the linear forms. Let Λ=b 2 logα 2 -b 1 logα 1 -b 3 logα 3 ≠0 with b 1 ,b 2 ,b 3 positive integers and α 1 ,α 2 ,α 3 positive multiplicatively independent rational numbers greater ...
Bennett, Curtis D. +4 more
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Статистика и экономикаThe objective of the study is to develop a mathematical model and corresponding methodology that allows, based on available empirical observations (market data), in a comparative approach, to create an assessment of the market value of a single real ...
V. D. Kreshchensky +2 more
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Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms [PDF]
Acta Arithmetica, 1994 In order to compute all integer points on a Weierstraß equation for an elliptic curve \(E/\mathbb{Q}\), one may translate the linear relation between rational points on \(E\) into a linear form of elliptic logarithms. An upper bound for this linear form can be obtained by employing the Néron-Tate height function and a lower bound is provided by a ...
Stroeker, RJ (Roel), Tzanakis, N (Nikos)
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On Algebraic Numbers of Small Height: Linear Forms in One Logarithm
Journal of Number Theory, 1994 The authors establish a lower bound for \(|\alpha -1|\) where \(\alpha\) is a complex algebraic number \(\neq 1\). This lower bound is completely explicit in terms of the degree \(D\) of \(\alpha\) and its Mahler measure \(M(\alpha)\). Given any number \(\mu>0\) with \(\mu\geq \log M(\alpha)\), the authors prove \[ |\alpha -1|\geq \exp \Bigl\{- \bigl( \
Mignotte, M., Waldschmidt, M.
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On the number of linear forms in logarithms
Journal of Number Theory, 2007 8 ...
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Explicit lower bounds for linear forms in two logarithms [PDF]
Journal de théorie des nombres de Bordeaux, 2008 We give an explicit lower bound for linear forms in two logarithms. For this we specialize the so-called Schneider method with multiplicity described in [10]. We substantially improve the numerical constants involved in existing statements for linear forms in two logarithms, obtained from Baker’s method or Schneider’s method with multiplicity.
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Matrices whose coefficients are linear forms in logarithms
Journal of Number Theory, 1992 Denote by \(L\) the \({\mathbb{Q}}\)-vector space of complex numbers \(\ell\) such that \(e^{\ell}\) is an algebraic number, and by \({\mathcal L}\) the vector space generated by \(1\) and \(L\) over the field \(\overline\mathbb{Q}\) of algebraic numbers.
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