Additive Completion of Lacunary Sequences

To the memory of Pál Erdős

Thirty years ago I read the following question of Erdőos [4]:

"Does there exist a sequence with so that every sufficiently large number is of the form ? $10"

I sent my solution to Erdős in a letter (in Hungarian). He translated my letter into English and sent it to the Canadian Math. Bulletin; this became my first paper to appear.

In this paper we will find, among others, the best value of the constant c in the above question, which was also asked by Erdős.

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Received March 30, 2000

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ID="*" Supported by Hungarian National Foundation for Scientific Research, Grants No. T 025617 and T 29759.

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Ruzsa, I. Additive Completion of Lacunary Sequences. Combinatorica 21, 279–291 (2001). https://doi.org/10.1007/s004930100025

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  • AMS Subject Classification (2000) Classes:  11B13, 11B34, 11B83