On the sum of two powered numbers

2023/06/09 by Jörg Brüdern, Olivier Robert, Brüdern, Jörg +1
Computer Science · #11B13 #Computability, Logic, AI Algorithms #FOS: Mathematics #G.2.0 #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2306.12431

openalex publication_date 2023/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Fix a positive real number θ. The natural numbers m with largest square-free divisor not exceeding m^θ form a set \mathscrA, say. It is shown that whenever θ>1/2 then all large natural numbers n are the sum of two elements of \mathscrA. This is nearly best possible.

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