Research output per year
Research output per year
David Wakeham, David R. Wood
Research output: Chapter in Book/Report/Conference proceeding › Chapter (Book) › Other › peer-review
Fix integers b > a ≥ 1 with g:= gcd(a, b). A set S ⊆ N is {a, b}-multiplicative if ax ≠ by for all x, y ϵ S. For all n, we determine an {a, b}-multiplicative set with maximum cardinality in [n], and conclude that the maximum density of an {a, b}-multiplicative set is b/b+g. For A, B ⊆ N, a set S ⊆ N is {A, B}-multiplicative if for all a ϵ A and b ϵ B and x, y ϵ S, the only solutions to ax = by have a = b and x = y. For 1 < a < b < c and a, b, c coprime, we give a O(1) time algorithm to approximate the maximum density of an {{a}, {b, c}}-multiplicative set to arbitrary given precision.
Original language | English |
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Title of host publication | Integers: Annual Volume 2013 |
Publisher | Walter de Gruyter |
Pages | 392-401 |
Number of pages | 10 |
ISBN (Electronic) | 9783110298161 |
ISBN (Print) | 9783110298116 |
DOIs | |
Publication status | Published - 1 Jan 2014 |
Research output: Contribution to journal › Article › Research › peer-review