Revista Matemática Iberoamericana

Arithmetic properties of positive integers with fixed digit sum

Florian Luca

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Abstract

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.

Article information

Source
Rev. Mat. Iberoamericana, Volume 22, Number 2 (2006), 369-412.

Dates
First available in Project Euclid: 26 October 2006

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1161871343

Mathematical Reviews number (MathSciNet)
MR2294785

Zentralblatt MATH identifier
1154.11032

Subjects
Primary: 11A63: Radix representation; digital problems {For metric results, see 11K16}
Secondary: 11N64: Other results on the distribution of values or the characterization of arithmetic functions

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

Citation

Luca, Florian. Arithmetic properties of positive integers with fixed digit sum. Rev. Mat. Iberoamericana 22 (2006), no. 2, 369--412. https://projecteuclid.org/euclid.rmi/1161871343


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