# Revista Matemática Iberoamericana

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**Volume 22, Issue 2, 2006, pp. 369–412**

**DOI: 10.4171/RMI/461**

Published online: 2006-08-31

Arithmetic properties of positive integers with fixed digit sum

Florian Luca^{[1]}(1) UNAM, Campus Morelia, Michoacán, Mexico

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.

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

Luca Florian: Arithmetic properties of positive integers with fixed digit sum. *Rev. Mat. Iberoam.* 22 (2006), 369-412. doi: 10.4171/RMI/461