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September, 2006 Arithmetic properties of positive integers with fixed digit sum
Florian Luca
Rev. Mat. Iberoamericana 22(2): 369-412 (September, 2006).


In this paper, we look at various arithmetic properties of the set of those positive integers $n$ whose sum of digits in a fixed base $b>1$ is a fixed positive integers $s$. For example, we prove that such integers can have many prime factors, that they are not very smooth, and that most such integers have a large prime factor dividing the value of their Euler $\phi$ function.


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Florian Luca . "Arithmetic properties of positive integers with fixed digit sum." Rev. Mat. Iberoamericana 22 (2) 369 - 412, September, 2006.


Published: September, 2006
First available in Project Euclid: 26 October 2006

zbMATH: 1154.11032
MathSciNet: MR2294785

Primary: 11A63
Secondary: 11N64

Keywords: linear forms in logarithms , smooth numbers , subspace theorem , sum of digits

Rights: Copyright © 2006 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.22 • No. 2 • September, 2006
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