Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  863.11014
Autor:  Burr, Stefan A.; Erdös, Paul; Graham, Ronald L.; Li, W.Wen-Ching
Title:  Complete sequences of sets of integer powers. (In English)
Source:  Acta Arith. 77, No.2, 133-138 (1996).
Review:  For a sequence S = (s1, s2, ...) of positive integers, define \Sigma (S): = {sumooi = 1 \epsiloni si: \epsiloni = 0 or 1, sumooi = 1 \epsiloni < oo}. Call S complete if \Sigma (S) contains all sufficiently large integers. It has been known for some time that if gcd (a,b) = 1 then the (nondecreasing) sequence formed from the values as bt with s0 \leq s, t0 \leq t \leq f (s0, t0) is complete, where s0 and t0 are arbitrary, and f(s0, t0) is sufficiently large.
In this note we consider the analogous question for sequences formed from pure powers of integers.
Reviewer:  S.A.Burr (New York)
Classif.:  * 11B83 Special sequences of integers and polynomials
                   11B13 Additive bases
Keywords:  complete sequences; sets of integer powers; bases; sumsets

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