A Note on the Recurrence Theorem
Filipczak, Tomasz (2015-12-07T12:09:00Z)
Acta Universitatis Lodziensis. Folia Mathematica
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Filipczak, Tomasz (2015-12-07T12:09:00Z)
Acta Universitatis Lodziensis. Folia Mathematica
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David Boyd (1979)
Acta Arithmetica
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Diego Marques, Alain Togbé (2011)
Colloquium Mathematicae
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In 2000, Florian Luca proved that F₁₀ = 55 and L₅ = 11 are the largest numbers with only one distinct digit in the Fibonacci and Lucas sequences, respectively. In this paper, we find terms of a linear recurrence sequence with only one block of digits in its expansion in base g ≥ 2. As an application, we generalize Luca's result by finding the Fibonacci and Lucas numbers with only one distinct block of digits of length up to 10 in its decimal expansion.
Cossali, G.E. (2003)
Journal of Integer Sequences [electronic only]
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Dubickas, A. (2005)
Journal of Mathematical Sciences (New York)
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Lenny Jones (2012)
Acta Arithmetica
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Alexey Stakhov (2012)
Visual Mathematics
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Ji-Cai Liu, He-Xia Ni (2021)
Czechoslovak Mathematical Journal
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We prove two supercongruences involving Almkvist-Zudilin sequences, which were originally conjectured by Z.-H. Sun (2020).
Hans Carstens (1975)
Fundamenta Mathematicae
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Mercer, A.McD. (1978)
International Journal of Mathematics and Mathematical Sciences
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Hiroyuki Okazaki (2015)
Formalized Mathematics
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In this article we formalize negligible functions that play an essential role in cryptology [10], [2]. Generally, a cryptosystem is secure if the probability of succeeding any attacks against the cryptosystem is negligible. First, we formalize the algebra of polynomially bounded sequences [20]. Next, we formalize negligible functions and prove the set of negligible functions is a subset of the algebra of polynomially bounded sequences. Moreover, we then introduce equivalence relation...
Barbero, Stefano, Cerruti, Umberto, Murru, Nadir (2010)
Journal of Integer Sequences [electronic only]
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Kit-Ho Mak, Alexandru Zaharescu (2016)
Acta Arithmetica
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In an earlier paper Gyarmati introduced the notion of f-correlation for families of binary pseudorandom sequences as a measure of randomness in the family. In this paper we generalize the f-correlation to families of pseudorandom sequences of k symbols and study its properties.
Horst Alzer, Florian Luca (2022)
Mathematica Bohemica
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We extend an inequality for Fibonacci numbers published by P. G. Popescu and J. L. Díaz-Barrero in 2006.