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