Remarks on additive representations of natural numbers

2023/09/07 by Li, Runbo
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2309.03218

Abstract

For two relatively prime square-free positive integers a and b, we study integers of the form a p+b P₂ and give a new lower bound for the number of such representations, where a p and b P₂ are both square-free, p denote a prime, and P₂ has at most two prime factors. We also consider some special cases where p is small, p and P₂ are within short intervals, p and P₂ are within arithmetical progressions and a Goldbach-type upper bound result. Our new results generalize and improve previous results.

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