On a problem of sidon in additive number theory, and on some related problems

  title={On a problem of sidon in additive number theory, and on some related problems},
  author={Paul Erd{\"o}s and Paul Tur{\'a}n},
  journal={Journal of The London Mathematical Society-second Series},
  • P. Erdös, P. Turán
  • Published 1 October 1941
  • Mathematics
  • Journal of The London Mathematical Society-second Series
To the memory of S. Sidon. Let 0 < a, < a,. .. be an infinite sequence of positive integers. Denote by f(n) the number of solutions of n=a i +a;. About twenty years ago, SIDON 1) raised the question wether there exists a sequence a; satisfying f(n) > 0 for all n > 1 and lim f(n)'nE = 0 for all t > 0. In the present note, I will construct such a sequence. In fact, my sequence will satisfy (1) 0 < f(n) < c l log n for all n > l. (The c's will denote suitable positive absolute constants .) It… 
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