Cite this article as:

Naumenko A. P. On the Distribution of the Numbers with Binary Expansions of a Special Type in Arithmetic Progressions. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2008, vol. 8, iss. 4, pp. 34-37. DOI: https://doi.org/10.18500/1816-9791-2008-8-4-34-37

Language: 
Russian
Heading: 
Mathematics
UDC: 
511

On the Distribution of the Numbers with Binary Expansions of a Special Type in Arithmetic Progressions

Authors: 
Naumenko Anton Pavlovich, Belgorod State National Research University, 85, Pobedy st., 308015, Belgorod, Russia , naumenko_anton90@mail.ru, gritsenko@bsu.edu.ru
Abstract: 

Let 2 be the primitive root mod p. Let N0 be a set of natural numbers whose binary expansions contain even numbers of 1. Numbers from N0 are uniformly distributed in arithmetic progressions with the difference p.

Key words: 
binary expansion, trigonometric sum
DOI: 
https://doi.org/10.18500/1816-9791-2008-8-4-34-37
References

1. Gelfond A.O. Sur les nombres qui ont des proprietes additives et multiplicatives donnies // Acta Arith. 1968. V. XIII. P. 259–265.

2. Айерленд К., Роузен М. Классическое введение в современную теорию чисел. М.: Мир, 1987. 

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