On a question of Erdos and Graham

I. E. Shparlinski

doi:10.1007/s00013-002-8269-2

On a question of Erdos and Graham

I. E. Shparlinski^*

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

We prove that for any ε > 0 there is k(ε) such that for any prime p and any integer c there exist k ≦ k(ε) pairwise distinct integers x_i with 1 ≦ x_i ≦ p^ε, i = 1,...,k, and such that ∑_i=1^k1/x_i ≡ c (mod p). This gives a positive answer to a question of Erdos and Graham.

Original language	English
Pages (from-to)	445-448
Number of pages	4
Journal	Archiv der Mathematik
Volume	78
Issue number	6
DOIs	https://doi.org/10.1007/s00013-002-8269-2
Publication status	Published - 1 Jun 2002

Access to Document

10.1007/s00013-002-8269-2

Cite this

@article{601a3f9e158748978396439d0ed49888,

title = "On a question of Erdos and Graham",

abstract = "We prove that for any ε > 0 there is k(ε) such that for any prime p and any integer c there exist k ≦ k(ε) pairwise distinct integers xi with 1 ≦ xi ≦ pε, i = 1,...,k, and such that ∑i=1k1/xi ≡ c (mod p). This gives a positive answer to a question of Erdos and Graham.",

author = "Shparlinski, {I. E.}",

year = "2002",

month = jun,

day = "1",

doi = "10.1007/s00013-002-8269-2",

language = "English",

volume = "78",

pages = "445--448",

journal = "Archiv der Mathematik",

issn = "0003-889X",

publisher = "Birkhauser Verlag Basel",

number = "6",

}

TY - JOUR

T1 - On a question of Erdos and Graham

AU - Shparlinski, I. E.

PY - 2002/6/1

Y1 - 2002/6/1

N2 - We prove that for any ε > 0 there is k(ε) such that for any prime p and any integer c there exist k ≦ k(ε) pairwise distinct integers xi with 1 ≦ xi ≦ pε, i = 1,...,k, and such that ∑i=1k1/xi ≡ c (mod p). This gives a positive answer to a question of Erdos and Graham.

AB - We prove that for any ε > 0 there is k(ε) such that for any prime p and any integer c there exist k ≦ k(ε) pairwise distinct integers xi with 1 ≦ xi ≦ pε, i = 1,...,k, and such that ∑i=1k1/xi ≡ c (mod p). This gives a positive answer to a question of Erdos and Graham.

UR - http://www.scopus.com/inward/record.url?scp=0036625277&partnerID=8YFLogxK

U2 - 10.1007/s00013-002-8269-2

DO - 10.1007/s00013-002-8269-2

M3 - Article

AN - SCOPUS:0036625277

SN - 0003-889X

VL - 78

SP - 445

EP - 448

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 6

ER -

On a question of Erdos and Graham

Abstract

Access to Document

Other files and links

Fingerprint

Cite this