Permanent problem IDPPL 044
Primitive sets
Let A⊂ (1,∈fty) be a countably infinite set such that for all x≠ y∈ A and integers k≥ 1 we have | kx -y| ≥ 1. Does this imply that A is sparse? In particular, does this imply that ∑_(x∈ A)(1/xlog x)<∈fty or ∑_{\substack{x <n\\ x∈ A}}(1/x)=o(log n)?
Let A⊂ (1,∈fty) be a countably infinite set such that for all x≠ y∈ A and integers k≥ 1 we have | kx -y| ≥ 1. Does this imply that A is sparse? In particular, does this imply that ∑_(x∈ A)(1/xlog x)<∈fty or ∑_{\substack{x <n\\ x∈ A}}(1/x)=o(log n)?
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