EUDML

In an earlier paper [9], the authors discussed some solved and unsolved problems in combinatorial number theory. First we will give an update of some of these problems. In the remaining part of this paper we will discuss some further problems of the two authors.

On prime factors of integers of the form (ab+1)(bc+1)(ca+1)

K. Győry; A. Sárközy — 1997

Acta Arithmetica

1. Introduction. For any integer n > 1 let P(n) denote the greatest prime factor of n. Győry, Sárközy and Stewart [5] conjectured that if a, b and c are pairwise distinct positive integers then (1) P((ab+1)(bc+1)(ca+1)) tends to infinity as max(a,b,c) → ∞. In this paper we confirm this conjecture in the special case when at least one of the numbers a, b, c, a/b, b/c, c/a has bounded prime factors. We prove our result in a quantitative form by showing that if is a finite set of triples (a,b,c)...

Problems and Results on Additive Properties of General Sequemnces, V.

P. Erdös; A. Sárközy; V.T. Sós — 1986

Monatshefte für Mathematik

On partitions without small parts

J.-L. Nicolas; A. Sárközy — 2000

Journal de théorie des nombres de Bordeaux

Let $r (n, m)$ denote the number of partitions of $n$ into parts, each of which is at least $m$ . By applying the saddle point method to the generating series, an asymptotic estimate is given for $r (n, m)$ , which holds for $n \to \infty$ , and $1 \leq m \leq c_{1} \frac{n}{{(log n)}^{c_{2}}}$ .

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On isolated, respectively consecutive large values of arithmetic functions

On sums and products of residues modulo p

On Irregularities of Distribution in Shifts and Dilations of Integer Sequences. I.

On divisors of sums of integers. II.

On Differences and sums of Integers, II

Some solved and unsolved problems in combinatorial number theory, ii

On prime factors of integers of the form (ab+1)(bc+1)(ca+1)

Problems and Results on Additive Properties of General Sequemnces, V.

On partitions without small parts

On the number of pairs of partitions of n without common subsums

On pseudorandom binary lattices

Sommes de sous-ensembles

On the number of prime factors of integers of the form ab + 1