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On some questions of Erdős and Graham about Egyptian fractions
Author(s) -
Croot Ernest S.
Publication year - 1999
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300007828
Subject(s) - mathematics , mathematics education
In this paper it is proved that, for x sufficiently large, every integer m with 1 ⩽ m ⩽ [∑ 1 ⩽ n ⩽ x1 n − 9 2( log log x ) 2 ( 1 + o ( 1 ) )log x]can be written as m = Σ 1≤ n ≤ x ε n / n , where ε i , = 0 or 1.