A cellular automaton on a torus.
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Cobeli, C.I., Crâşmaru, M., Zaharescu, A. (2000)
Portugaliae Mathematica
Chapman, Scott T., Smith, William W. (2005)
Integers
Xingwu Xia, Yongke Qu, Guoyou Qian (2014)
Colloquium Mathematicae
Let G be an additive abelian group of order k, and S be a sequence over G of length k+r, where 1 ≤ r ≤ k-1. We call the sum of k terms of S a k-sum. We show that if 0 is not a k-sum, then the number of k-sums is at least r+2 except for S containing only two distinct elements, in which case the number of k-sums equals r+1. This result improves the Bollobás-Leader theorem, which states that there are at least r+1 k-sums if 0 is not a k-sum.
O'Bryant, Kevin (2004)
The Electronic Journal of Combinatorics [electronic only]
Scott Ahlgren (2003)
Acta Arithmetica
L. Kuipers, Jau-Shyong Shiue (1972)
Elemente der Mathematik
Dearden, Bruce, Iiams, Joel, Metzger, Jerry (2011)
Journal of Integer Sequences [electronic only]
Burke, John R. (1993)
International Journal of Mathematics and Mathematical Sciences
Piotr Miska (2015)
Colloquium Mathematicae
A prime number p is called a Schenker prime if there exists n ∈ ℕ₊ such that p∤n and p|aₙ, where is a so-called Schenker sum. T. Amdeberhan, D. Callan and V. Moll formulated two conjectures concerning p-adic valuations of aₙ when p is a Schenker prime. In particular, they conjectured that for each k ∈ ℕ₊ there exists a unique positive integer such that for each nonnegative integer m. We prove that for every k ∈ ℕ₊ the inequality v₅(aₙ) ≥ k has exactly one solution modulo . This confirms the...
Jiří Klaška (2008)
Acta Mathematica Universitatis Ostraviensis
Such problems as the search for Wieferich primes or Wall-Sun-Sun primes are intensively studied and often discused at present. This paper is devoted to a similar problem related to the Tribonacci numbers.
Katalin Gyarmati, Imre Z. Ruzsa (2012)
Acta Arithmetica
Akbik, Safwan (1991)
International Journal of Mathematics and Mathematical Sciences
Cao, Huiqin (2006)
The Electronic Journal of Combinatorics [electronic only]
Bialostocki, Arie, Tran Dinh Luong (2009)
Integers
Gautami Bhowmik, Jan-Christoph Schlage-Puchta (2010)
Acta Arithmetica
Brad Wilson (1998)
Acta Arithmetica
González, Samuel, González, Leida, Ordaz, Oscar (2009)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
Liu, Shu-Chung, Yeh, Jean C.-C. (2010)
Journal of Integer Sequences [electronic only]
Gautami Bhowmik, Jan-Christoph Schlage-Puchta (2011)
Acta Arithmetica
Milan Paštéka (1992)
Mathematica Slovaca
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