, Volume 21, Issue 2, pp 279-291

Additive Completion of Lacunary Sequences

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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.

Received March 30, 2000
ID="*" Supported by Hungarian National Foundation for Scientific Research, Grants No. T 025617 and T 29759.