Wyniki wyszukiwania

1

On sums and products of residues modulo p

100%

Sárközy A.

Acta Arithmetica

|

2005

|

tom 118

|

nr 4

403-409

2

On isolated, respectively consecutive large values of arithmetic functions

100%

Sárközy A.

Acta Arithmetica

|

1994

|

tom 66

|

nr 3

269-295

3

Some solved and unsolved problems in combinatorial number theory, ii

64%

Erdős P., Sárközy A.

Colloquium Mathematicum

|

1993

|

tom 65

|

nr 2

201-211

EN

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.

4

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

64%

Győry K., Sárközy A.

Acta Arithmetica

|

1997

|

tom 79

|

nr 2

163-171

EN

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 𝓐 is a finite set of triples (a,b,c) of positive integers a, b, c with the property mentioned above then for some (a,b,c) ∈ 𝓐, (1) is greater than a constant times log|𝓐|loglog|𝓐|, where |𝓐| denotes the cardinality of 𝓐 (cf. Corollary to Theorem 1). Further, we show that this bound cannot be replaced by $|𝓐|^ε$ (cf. Theorem 2). Recently, Stewart and Tijdeman [9] proved the conjecture in another special case. Namely, they showed that if a ≥ b > c then (1) exceeds a constant times log((loga)/log(c+1)). In the present paper we give an estimate from the opposite side in terms of a (cf. Theorem 3).

5

On pseudorandom binary lattices

52%

Hubert P., Mauduit C., Sárközy A.

Acta Arithmetica

|

2006

|

tom 125

|

nr 1

51-62

6

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

52%

Erdős P., Nicolas J.-L., Sárközy A.

Colloquium Mathematicum

|

1992

|

tom 63

|

nr 1

61-83

7

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

52%

Győry K., Sárközy A., Stewart C.

Acta Arithmetica

|

1996

|

tom 74

|

nr 4

365-385

8

On the divisibility properties of sequences of integers (II)

39%

Erdös P., Sárközy A., Szemerédi E.

Acta Arithmetica

|

1968

|

tom 14

|

nr 1

1-12

9

On the divisibility properties of integers (I)

33%

Erdös P., Sárközy A., Szemerédi E.

Acta Arithmetica

|

1965-1966

|

tom 11

|

nr 4

411-418

10

Some asymptotic formulas on generalized divisor functions, III

32%

Sárközy A., Erdös P.

Acta Arithmetica

|

1982

|

tom 41

|

nr 4

395-411

11

Über ein Problem von Erdös und Moser

26%

Sárközy A., Szemerédi E.

Acta Arithmetica

|

1965-1966

|

tom 11

|

nr 2

205-208

12

On sums of sequences of integers, I

26%

Balog A., Sárközy A.

Acta Arithmetica

|

1984-1985

|

tom 44

|

nr 1

73-86

13

On a theorem of Erdös and Fuchs

26%

Sárközy A.

Acta Arithmetica

|

1980

|

tom 37

|

nr 1

333-338

14

Über totalprimitive Folgen

23%

Sárközy A.

Acta Arithmetica

|

1962-1963

|

tom 8

|

nr 1

21-31

15

Über reduzible Folgen

20%

Sárközy A.

Acta Arithmetica

|

1964-1965

|

tom 10

|

nr 4

399-408

Ograniczanie wyników

On sums and products of residues modulo p

On isolated, respectively consecutive large values of arithmetic functions

Some solved and unsolved problems in combinatorial number theory, ii

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

On pseudorandom binary lattices

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

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

On the divisibility properties of sequences of integers (II)

On the divisibility properties of integers (I)

Some asymptotic formulas on generalized divisor functions, III

Über ein Problem von Erdös und Moser

On sums of sequences of integers, I

On a theorem of Erdös and Fuchs

Über totalprimitive Folgen

Über reduzible Folgen