JournalsrmiVol. 22, No. 2pp. 369–412

Arithmetic properties of positive integers with fixed digit sum

  • Florian Luca

    UNAM, Campus Morelia, Michoacán, Mexico
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Abstract

In this paper, we look at various arithmetic properties of the set of those positive integers nn whose sum of digits in a fixed base b>1b>1 is a fixed positive integers ss. 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 ϕ\phi function.

Cite this article

Florian Luca, Arithmetic properties of positive integers with fixed digit sum. Rev. Mat. Iberoam. 22 (2006), no. 2, pp. 369–412

DOI 10.4171/RMI/461