Article contents
On multiplicative representations of integers
Published online by Cambridge University Press: 09 April 2009
Abstract
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
- Copyright
- Copyright © Australian Mathematical Society 1976
References
- 2
- Cited by