On -complete sequences modulo l
Tom 213 / 2024
Acta Arithmetica 213 (2024), 369-378
MSC: Primary 11B75
DOI: 10.4064/aa230602-31-10
Opublikowany online: 27 February 2024
Streszczenie
A sequence \mathcal {T} of positive integers is called d-complete modulo l if for every integer 0\leq u\leq l-1, there exists an integer v with vl+u \gt 0 such that vl+u can be represented as the sum of distinct terms from \mathcal {T}, where no one divides any other. Recently, Chen and Yu (2023) proved that \{m^an^b:a,b=0,1,2,\ldots \} is d-complete modulo l if l,m,n are pairwise coprime with l,m,n\geq 2, and posed the following problem: characterize all positive integers l,m,n such that \{m^an^b:a,b=0,1,2,\ldots \} is d-complete modulo l. We give an answer to this problem.
