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Displaying 61 – 80 of 136

On a system of equations with primes

Paolo Leonetti, Salvatore Tringali (2014)

Journal de Théorie des Nombres de Bordeaux

Given an integer $n \geq 3$ , let $u_{1}, ..., u_{n}$ be pairwise coprime integers $\geq 2$ , $𝒟$ a family of nonempty proper subsets of ${1, ..., n}$ with “enough” elements, and $ε$ a function $𝒟 \to {\pm 1}$ . Does there exist at least one prime $q$ such that $q$ divides $\prod_{i \in I} u_{i} - ε (I)$ for some $I \in 𝒟$ , but it does not divide $u_{1} \dots u_{n}$ ? We answer this question in the positive when the $u_{i}$ are prime powers and $ε$ and $𝒟$ are subjected to certain restrictions.We use the result to prove that, if $ε_{0} \in {\pm 1}$ and $A$ is a set of three or more primes that contains all prime divisors of any number of the form $\prod_{p \in B} p - ε_{0}$ for...

On an algorithm which produces the g.c.d. of a set of n (n>2) integers in a simultaneous manner.

P. Laborde (1967)

Gaceta Matemática

On an extension of Kronecker's function

Rao, K. Nageswara (1968)

Portugaliae mathematica

On certain arithmetic functions involving the greatest common divisor

Ekkehard Krätzel, Werner Nowak, László Tóth (2012)

Open Mathematics

The paper deals with asymptotics for a class of arithmetic functions which describe the value distribution of the greatest-common-divisor function. Typically, they are generated by a Dirichlet series whose analytic behavior is determined by the factor ζ2(s)ζ(2s − 1). Furthermore, multivariate generalizations are considered.

On divisibility of some power sums.

Lengyel, Tamás (2007)

Integers

On exceptions to Szegedy's theorem

M. Chaimovich, G. Freimann, J. Schönheim (1987)

Acta Arithmetica

On $f$ -thin sets

Pavel Kostyrko (1982)

Časopis pro pěstování matematiky

On happy factorizations.

Conway, J.H. (1998)

Journal of Integer Sequences [electronic only]

On K-Stage Euclidean algorithms for Galois extensions of Q.

David A. Clark (1996)

Manuscripta mathematica

On multiplicatively e-perfect numbers.

Sándor, József (2004)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On prime factors of sums of integers I

K. Györy, C. L. Stewart, R. Tijdeman (1986)

Compositio Mathematica

On prime factors of sums of integers III

Kalman Győry, C. Stewart, R. Tijdeman (1988)

Acta Arithmetica

On sets S.

P. Laborde (1970)

Gaceta Matemática

On some extensions of Jordan's arithmetic functions.

Andrica, Dorin, Piticari, Mihai (2004)

Acta Universitatis Apulensis. Mathematics - Informatics

On the degree of regularity of generalized van der Waerden triples.

Fox, Jacob, Radoičić, Radoš (2005)

Integers

On the diameter of sets of almost powers

B. M. M. de Weger, C. E. van de Woestijne (1999)

Acta Arithmetica

On the Exponent Average of Integer Sequences.

J.W. Sander (1995)

Monatshefte für Mathematik

On the integers $x_{i}$ for which $x_{i} ∣ x_{1} \dots x_{i - 1} x_{i} \dots x_{n} + 1$ holds

Jaroslav Janák, Ladislav Skula (1978)

Mathematica Slovaca

On the least common multiple of Lucas subsequences

Shigeki Akiyama, Florian Luca (2013)

Acta Arithmetica

We compare the growth of the least common multiple of the numbers $u_{a_{1}}, . . ., u_{a_{n}}$ and $| u_{a_{1}} \dots u_{a_{n}} |$ , where ${(u_{n})}_{n \geq 0}$ is a Lucas sequence and ${(a_{n})}_{n \geq 0}$ is some sequence of positive integers.

On the multiplicative order of $a^{n}$ modulo $n$ .

Chappelon, Jonathan (2010)

Journal of Integer Sequences [electronic only]

Currently displaying 61 – 80 of 136

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