number-theory / Additive and multiplicative combinatorics

Nathanson's Problems on Product Intersection Sets

Nathanson asked which subsets of $\mathbb{N}$ can occur as product intersection sets of a family of semigroup subsets, for arbitrary and for decreasing families (his Problems 10 and 11). Both are solved by complete classifications.

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number-theoryApr 20, 2026Significance 8/100Registry: lean checked

Nathanson's Problems on Product Intersection Sets

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Nathanson asked which subsets of $\mathbb{N}$ can occur as product intersection sets of a family of semigroup subsets, for arbitrary and for decreasing families (his Problems 10 and 11). Both are solved by complete classifications.

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Nathanson asked which subsets of $\mathbb{N}$ can occur as product intersection sets of a family of semigroup subsets, for arbitrary and for decreasing families (his Problems 10 and 11). Both are solved by complete classifications.

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