Representation of integers by near quadratic sequences

Labib Haddad, Charles Helou

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

Following a statement of the well-known Erdo{double acute}s-Turán conjecture, Erdo{double acute}s mentioned the following even stronger conjecture: if the n-th term an of a sequence A of positive integers is bounded by αn2, for some positive real constant α, then the number of representations of n as a sum of two terms from A is an unbounded function of n. Here we show that if an differs from αn2 (or from a quadratic polynomial with rational coefficients q(n)) by at most o(√log n), then the number of representations function is indeed unbounded.

Original languageEnglish (US)
JournalJournal of Integer Sequences
Volume15
Issue number8
StatePublished - Oct 23 2012

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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