Revista Matemática Iberoamericana
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Published online: 2006-08-31
Arithmetic properties of positive integers with fixed digit sumFlorian Luca (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