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Primitive Sequences and Sets of Multiples

In: Sequences

Author

Listed:
  • H. Halberstam

    (University of Illinois, Department of Mathematics)

  • K. F. Roth

    (Imperial College of Science and Technology, Department of Mathematics)

Abstract

Throughout this chapter A = {a i } will denote a subsequence of the sequence of natural numbers. We consider the set ℬ = ℬ(A) consisting of all the distinct positive multiples of elements of A. We note that ℬ is the positive part of the union, taken over all elements a i of A, of the congruence classes 0 (mod a i ). Whilst none of our arguments will depend on ordering ℬ, it will often be convenient (to facilitate description and for reasons of notation) to imagine ℬ to be ordered according to magnitude and to refer to it as a ‘sequence’.

Suggested Citation

  • H. Halberstam & K. F. Roth, 1983. "Primitive Sequences and Sets of Multiples," Springer Books, in: H. Halberstam & K. F. Roth (ed.), Sequences, chapter 0, pages 238-274, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-8227-0_5
    DOI: 10.1007/978-1-4613-8227-0_5
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