On Thin Sum-Product Bases

Besides various asymptotic results on the concept of sum-product bases in the set of non-negative integers ℕ, we investigate by probabilistic arguments the existence of thin sets A, A ′ of non-negative integers such that AA + A = ℕ and A ′ A ′ + A ′ A ′ = ℕ.

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Bibliographische Detailangaben
Veröffentlicht in:	Combinatorica (Budapest. 1981) 2022-04, Vol.42 (2), p.165-202
Hauptverfasser:	Hennecart, François, Prakash, Gyan, Pramod, Eyyunni
Format:	Artikel
Sprache:	eng
Schlagworte:	Combinatorics Integers Mathematics Mathematics and Statistics Number Theory Original Paper
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	Besides various asymptotic results on the concept of sum-product bases in the set of non-negative integers ℕ, we investigate by probabilistic arguments the existence of thin sets A, A ′ of non-negative integers such that AA + A = ℕ and A ′ A ′ + A ′ A ′ = ℕ.
ISSN:	0209-9683 1439-6912
DOI:	10.1007/s00493-021-4195-4