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On multiplicative representations of integers

Published online by Cambridge University Press:  09 April 2009

P. Erdös  and
A. Szemerédi
P. Erdös
Affiliation:
Department of Computer Science, Stanford University, California, U.S.A.
A. Szemerédi
Affiliation:
Department of Computer Science, Stanford University, California, U.S.A.
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Abstract

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Let 1 ≦ a1 < … < ak ≦ x; b1 < … b1 ≦ x. Assume that the number of solutions of a1b1 = m is less than c. The authors prove that then . They also give a simple proof of Szemerédi's theorem: If the products aibj are all distinct then . They conjecture that (2) holds for c2 = 1 + ε if x > x0(ε). Several other unsolved problems are stated.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 4 , June 1976 , pp. 418 - 427
Copyright
Copyright © Australian Mathematical Society 1976

References

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