Mathematics

On an Additive Problem with Squarefree Numbers

Authors: Goryashin D. V.
An asymptotic formula for the number of representations of a positive integer N in the form q1 + q2 + [®q3] is obtained, where q1, q2, q3 are squarefree numbers and ® > 1 is a fixed irrational algebraic number.

Arithmetic Properties of Generalized Fibonacci Sequence and Their Consequences

Authors: Vassilyev A. N.
In this paper we obtain some arithmetic properties of generalized Fibonacci sequence and consider their applications.

On Classes of Groupoids of Relations with Diophantine Operations

Authors: Bredikhin D. A.
In the paper the bases of identities of varieties generated by classes of groupoids of the binary relations with diophantine operations are found.

Полупростые градуированные кольца

Authors: Balaba I. N., Krasnova E. N.
The graded version ofWedderburn–Artin theorem is obtained. It gives description of semisimpleG-graded ring for arbitrary groupG. Homological classification of graded semisimple rings is given.

Mathematical life of G. I. Arkhipov

Authors: Chubarikov V. N.
This paper presents the most important discoveries made by outstanding mathematician G. I. Arhkipov since the end of 60s to the middle of 2000s.

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