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

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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.",

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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.

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On a question of Erdos and Graham

Abstract

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