On the Distribution in Residue Classes of Integers with a Fixed Sum of Digits |
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| Authors: | Christian Mauduit Carl Pomerance András Sárközy |
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| Institution: | (1) Institut de Mathématiques de Luminy, UPR 9016 CNRS, 163, Avenue de Luminy, Case 907, F-13288 Marseille Cedex 9, France;(2) Department of Mathematics, Dartmouth College, Hanover, New Hampshire, 03755;(3) Department of Algebra and Number Theory, Eötvös Loránd University, H-1117 Budapest, Pázmány Péter sétány 1/C, Hungary |
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| Abstract: | We give an asymptotic formula for the distribution of those integers n in a residue class, such that n has a fixed sum of base-g digits, with some uniformity over the choice of the modulus and g. We then use this formula to solve the problem of I. Niven of giving an asymptotic formula for the distribution of those integers n divisible by the sum of their base-g digits. Our results also allow us to give a stronger form of a result of M. Olivier dealing with the distribution of integers with a given gcd with their sum of base-g digits.For our friend Jean-Louis Nicolas on his sixtieth birthdayResearch partially supported by the Hungarian National Foundation for Scientific Research, Grant No. T029759, and “Balaton” French-Hungarian exchange program F-18/00.2000 Mathematics Subject Classification: Primary—11A63 |
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| Keywords: | sum-of-digits function Niven numbers |
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