On sums of distinct powers of 3 and 4
Author(s)
Maximilian F. Hasler
Date issued
2024
In
Combinatorics and Number Theory
Vol
13
No
2
From page
141
To page
148
Reviewed by peer
true
Subjects
sum of powers Erdős problems additive problems
Abstract
In 1996 Erdős conjectured that the set Σ(Pow({3,4}),1) defined as the sums of distinct powers of 3 and distinct powers of 4 has positive asymptotic density. We investigate some structure properties of this set. We also prove some asymptotic estimates for its counting function P{3,4}(x). In particular we prove that P{3,4}(x)≫x^0.97777, improving an old estimate of Melfi.
Later version
https://msp.org/cnt/2024/13-2/p04.xhtml
Publication type
journal article
File(s)