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11-XX Number theory
11Bxx Sequences and sets
11B75 Other combinatorial number theory

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Displaying 41 – 60 of 281

Barycentric Ramsey numbers for small graphs.

González, Samuel, González, Leida, Ordaz, Oscar (2009)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Behrend-type constructions for sets of linear equations

Asaf Shapira (2006)

Acta Arithmetica

Binary linear forms over finite sets of integers

Melvyn B. Nathanson, Kevin O'Bryant, Brooke Orosz, Imre Ruzsa, Manuel Silva (2007)

Acta Arithmetica

Blocks and progressions in subset sum sets

Vsevolod F. Lev (2003)

Acta Arithmetica

Catalan-Zahlen und Wege in einem ganzzahligen Gitter.

P.J. Hilton, Jean Pedersen (1993)

Elemente der Mathematik

Central binomial sums, multiple Clausen values, and zeta values.

Borwein, Jonathan Michael, Broadhurst, David J., Kamnitzer, Joel (2001)

Experimental Mathematics

Choice Mappings of Certain Classes of Finite Sets.

Mordechai Lewin (1972)

Mathematische Zeitschrift

Combinatorial interpretations of convolutions of the Catalan numbers.

Tedford, Steven J. (2011)

Integers

Combinatorial proofs of some Moriarty-type binomial coefficient identities.

Shattuck, Mark (2006)

Integers

Congruences for Wolstenholme primes

Romeo Meštrović (2015)

Czechoslovak Mathematical Journal

A prime $p$ is said to be a Wolstenholme prime if it satisfies the congruence $(\binom{2 p - 1}{p - 1}) \equiv 1 (mod p^{4})$ . For such a prime $p$ , we establish an expression for $(\binom{2 p - 1}{p - 1}) (mod p^{8})$ given in terms of the sums $R_{i} : = \sum_{k = 1}^{p - 1} 1 / k^{i}$ ( $i = 1, 2, 3, 4, 5, 6)$ . Further, the expression in this congruence is reduced in terms of the sums $R_{i}$ ( $i = 1, 3, 4, 5$ ). Using this congruence, we prove that for any Wolstenholme prime $p$ we have $(\binom{2 p - 1}{p - 1}) \equiv 1 - 2 p \sum_{k = 1}^{p - 1} \frac{1}{k} - 2 p^{2} \sum_{k = 1}^{p - 1} \frac{1}{k^{2}} (mod p^{7}) .$ Moreover, using a recent result of the author, we prove that a prime $p$ satisfying the above congruence must necessarily be a Wolstenholme prime. Furthermore, applying a technique...

Continued fractions and Catalan problems.

Jani, Mahendra, Rieper, Robert G. (2000)

The Electronic Journal of Combinatorics [electronic only]

Convexity and a sum-product type estimate

Liangpan Li, Oliver Roche-Newton (2012)

Acta Arithmetica

Counting non-isomorphic maximal independent sets of the $n$ -cycle graph.

Bisdorff, Raymond, Marichal, Jean-Luc (2008)

Journal of Integer Sequences [electronic only]

Davenport constant with weights and some related questions.

Adhikari, Sukumar Das, Rath, Purusottam (2006)

Integers

Decimal expansion of $1 / p$ and subgroup sums.

Gupta, Ankit, Sury, S. (2005)

Integers

Decomposing rational numbers

Håkan Lennerstad, Lars Lundberg (2010)

Acta Arithmetica

Deriving divisibility theorems with Burnside's theorem.

Evans, Tyler J., Holt, Benjamin V. (2005)

Integers

Difference density and aperiodic sum-free sets.

Calkin, Neil J., Finch, Steven R., Flowers, Timothy B. (2005)

Integers

Digraphs Associated With Finite Rings

Aleksandar T. Lipkovski (2012)

Publications de l'Institut Mathématique

Discrepancy of sums of three arithmetic progressions.

Přívétivý, Aleš (2006)

The Electronic Journal of Combinatorics [electronic only]

Currently displaying 41 – 60 of 281

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