On a Problem of P. Erdös
Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 309-310
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P. Erdös asked the following problem: Does there exist an infinite sequence of integers a1<...satisfying for every x≥1 1 so that every integer is of the form 2k+ai [1]. The analogous questions can easily be answered affirmatively if the powers of 2 are replaced by the rth power.In this note we give a simple affirmative answer to the problem of Erdôs. Let c2 be a sufficiently small absolute constant. Our sequence A consists of all the integers of the form 2
Jr., I. Ruzsa. On a Problem of P. Erdös. Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 309-310. doi: 10.4153/CMB-1972-058-2
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author = {Jr., I. Ruzsa},
title = {On a {Problem} of {P.} {Erd\"os}},
journal = {Canadian mathematical bulletin},
pages = {309--310},
year = {1972},
volume = {15},
number = {2},
doi = {10.4153/CMB-1972-058-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-058-2/}
}
[1] 1. Erdös, P., Some results on additive number theory, Proc. Amer. Math. Soc. 5 (1954), 847-853 (see p. 853). See also Proc. of the Number Theory Conf. at Boulder, Colorado, 1963, Problem 33. Google Scholar
[2] 2. Lorentz, G. G., On a problem of additive number theory, Proc. Amer. Math. Soc. 5 (1954), 838-891. Google Scholar
[3] 3. Moser, L., On the additive completion of sets of integers, Proc. Symp. Pure Math., Amer. Math. Soc. 8 (1965), 175-180. Google Scholar
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