Integer Sum Sets Containing Long Arithmetic Progressions

Abstract

the Schnirelmann and lower asymptotic densities respectively of d. According to Schnirelmann theory (see [9]), if 1 > as/ > 0 and Oes/ then a(2s/) ^ 2a(s/)-a(s/) > a(s/); and if a(s/)^\ then 2s/ = No. From this it follows that if as/ > 0 then there exists a positive integer k such that s/ is a basis of order k (that is, ks/ = No). According to Kneser's… (More)

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