On additive representation of integers
type: Item
instance of: scholarly article
title: On additive representation of integers
zbMATH Open document ID: 0689.10050
DOI: 10.1007/BF01952060
published in: Acta Mathematica Hungarica
publication date: 1989-01-01T00:00:00Z
review text: For any integer \(m>1\) define P(m) to be the largest prime divisor of m. Put \(\alpha =4(9e^{1/2})^{-1}\). The following theorem is proved. Let \(\epsilon >0\) be any fixed number. Then there exists an \(N_ 0=N_ 0(\epsilon)\) such that every integer \(N>N_ 0\) can be expressed in the form \(N=a+b\) with \(a>1\), \(b>1\) and \(P(ab)<N^{\alpha +\epsilon}\). This beautiful result answers a question of P. Erdős in the affirmative. Erdős had asked the question with 1/3 in place of \(\alpha +\epsilon\). Apart from other things the proof involves a clever use of a complicated theorem of E. Fouvry.
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11B13
Mathematics Subject Classification ID: 11P99
zbMATH DE Number: 4128922
zbMATH Keywords: additive representation of integers
zbMATH Keywords: Erdős conjecture
zbMATH Keywords: Fouvry's theorem
author: Antal Balog
MaRDI profile type: Publication
cites work: Autour du théorème de Bombieri-Vinogradov. II
cites work: Q3737509
cites work: Q3699787
cites work: Q3737510
description: scientific article; zbMATH DE number 4128922