Result: On the Completeness of an Exponential Type Sequence: On the completeness of an exponential type sequence

Title:
On the Completeness of an Exponential Type Sequence: On the completeness of an exponential type sequence
Authors:
Norbert Hegyvári
Source:
Acta Mathematica Hungarica. 86:127-135
Publisher Information:
Springer Science and Business Media LLC, 2000.
Publication Year:
2000
Subject Terms:
Special sequences and polynomials, Other combinatorial number theory, complete sequences, 0101 mathematics, 01 natural sciences
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
1588-2632
0236-5294
DOI:
10.1023/a:1006799619623
Access URL:
https://link.springer.com/article/10.1023/A:1006799619623
Rights:
Springer Nature TDM
Accession Number:
edsair.doi.dedup.....3807da308dfde5bcb62fdab333f4712f
Database:
OpenAIRE

Further Information

Confirming a conjecture of P. Erdős, in 1959 \textit{B. J. Birch} [Proc. Camb. Philos. Soc. 55, 370-373 (1959; Zbl 0093.05003)] proved that for any coprime integers \(p, q>1\) every sufficiently large integer is a sum of distinct numbers of the form \(p^\alpha q^\beta \). The author shows that summands with the restriction \(\beta \leq K\) suffice for a suitable \(K=K(p,q)\), and exhibits such a bound \(K\). The bound is quadruply exponential in \(p\) and triply in \(q\), probably not the true order of magnitude.