Results 21 to 30 of about 6,941 (136)
Fibonacci Numbers with a Prescribed Block of Digits
Mathematics, 2020 In this paper, we prove that F 22 = 17711 is the largest Fibonacci number whose decimal expansion is of the form a b … b c … c . The proof uses lower bounds for linear forms in three logarithms of algebraic numbers and some tools from ...
Pavel Trojovský
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Larger Corner-Free Sets from Better NOF Exactly-$N$ Protocols
Discrete Analysis, 2021 Larger corner-free sets from better NOF exactly-$N$ protocols, Discrete Analysis 2021:19, 9 pp. If $G$ is an Abelian group, then a _corner_ in $G^2$ is a subset of the form $\{(x,y),(x+d,y),(x,y+d)\}$ with $d\ne 0$.
Nati Linial, Adi Shraibman
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On repdigits as product of $k$-Fibonacci and $k$-Lucas numbers [PDF]
Mathematica BohemicaFor an integer $k\geq2$, let $(F_n^{(k)})_{n\geq-(k-2)}$, $(L_n^{(k)})_{n \geq-(k-2)}$ be $k$-Fibonacci and $k$-Lucas sequences, respectively. For these sequences the first $k$ terms are $0,\ldots,0,1$ and $0,\ldots,0,2,1$, respectively, and each term ...
Safia Seffah +2 more
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On $k$-Pell numbers which are sum of two Narayana's cows numbers [PDF]
Mathematica BohemicaFor any positive integer $k\geq2$, let $(P_n^{(k)})_{n\geq2-k}$ be the $k$-generalized Pell sequence which starts with $0,\cdots,0,1$ ($k$ terms) with the linear recurrence P_n^{(k)} = 2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots+P_{n-k}^{(k)}\quad\text{for} n\
Kouèssi Norbert Adédji +2 more
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On Terms of Generalized Fibonacci Sequences which are Powers of their Indexes
Mathematics, 2019 The k-generalized Fibonacci sequence ( F n ( k ) ) n (sometimes also called k-bonacci or k-step Fibonacci sequence), with k ≥ 2 , is defined by the values 0 , 0 , … , 0 , 1 of starting k its terms and such way ...
Pavel Trojovský
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A kit for linear forms in three logarithms
Mathematics of Computation, 2023 We provide a technique to obtain explicit bounds for problems that can be reduced to linear forms in three complex logarithms of algebraic numbers. This technique can produce bounds significantly better than general results on lower bounds for linear forms in logarithms.
Mignotte, Maurice, Voutier, Paul
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A p-adic lower bound for a linear form in logarithms
International Journal of Number Theory, 2022 Linear forms in logarithms have an important role in the theory of Diophantine equations. In this paper, we prove explicit [Formula: see text]-adic lower bounds for linear forms in [Formula: see text]-adic logarithms of rational numbers using Padé approximations of the second kind.
Seppälä Louna, Palojärvi Neea
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International Journal of Electrochemical Science, 2013 In this work, an E-sensor basing on allosteric molecular beacons (aMBs) was designed for detection of Escherichia coli.(E. coli.)O157:H7 DNA. Without the target DNA, the aMB formed a stable hairpin structure which blocked the binding capability of the ...
Dongneng Jiang +4 more
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Linear forms in two logarithms and interpolation determinants [PDF]
Acta Arithmetica, 1994 The author provides a precise lower bound for the absolute value of a linear combination of two logarithms of real algebraic numbers with integer coefficients. This lower bound is explicit and improves in the real case an earlier result of \textit{M. Mignotte} and \textit{M. Waldschmidt} [Ann. Fac. Sci. Toulouse Math.
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Linear forms in logarithms and exponential Diophantine equations [PDF]
Hardy-Ramanujan Journal, 2020 This paper aims to show two things. Firstly the importance of Alan Baker's work on linear forms in logarithms for the development of the theory of exponential Diophantine equations. Secondly how this theory is the culmination of a series of greater and smaller discoveries.
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