# Scientific Journal of KubSAU

Polythematic online scientific journal
of Kuban State Agrarian University
ISSN 1990-4665

#### Name

Sergeev Eduard Alexandrovich

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#### Organization, job position

Kuban State University

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## Articles count: 6

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469 kb

abstract 1271703004 issue 127 pp. 113 – 125 31.03.2017 ru 711
The Euler function is very important in number theory and in Mathematics, however, the range of its values in the natural numbers has not been written off. The greatest value of the Euler function reaches on Prime numbers, furthermore, it is multiplicative. The value of the Euler function is closely associated with the values of the Moebius function and the function values of the sum of the divisors of the given natural number. The Euler function is linked with systems of public key encryption. The individual values of the Euler function behave irregularly because of the irregular distribution of primes in the natural numbers. This tract is illustrated in the article with charts; summatory function for the Euler function and its average value are more predictable. We prove the formula of Martinga and, based on it, we study the approximation accuracy of the average value of the Euler function with corresponding quadratic polynomial. There is a new feature associated with the average value of the Euler function and calculate intervals of its values. We also introduce the concept of density values of the Euler function and calculate its value on the interval of the natural numbers. It can be noted that the results of the behavior of the Euler function are followed by the results in the behavior of functions of sums of divisors of natural numbers and vice versa. We have also given the results of A.Z.Valfish and A.N.Saltykov on this subject
162 kb

#### ON THE NUMERATIONS OF THE FINITE PARTIALLY ORDERED SETS

abstract 1181604047 issue 118 pp. 805 – 816 29.04.2016 ru 805
In this article, we discuss various issues related to the formulas approximating the distribution function of prime numbers pi(x). This question has occupied many scholars, but the exact function is well approximated function pi(x) over the number of positive integers not. Based on certain hypotheses, we present a new function s(x) is very well approximated pi(x). The above article hypotheses are so important that their numerical validation and refinement for the lengths of the segments more in 1014 - one of the main areas related to the problem of approximation of the function pi(x) throughout the series of natural numbers. After analyzing the behaviors and constructs many functions, we are building the basis of the function s(x), which is well approximates the function pi(x) throughout the series of natural numbers. We also present a table of values for x, less or equal 1022 for the difference of s(x) - pi(x)
108 kb

#### FUNDAMENTAL THEOREM OF ARITHMETIC AND SOME OF ITS ASPECTS

abstract 1131509010 issue 113 pp. 127 – 132 30.11.2015 ru 885
In this article, we present the fundamental theorem of arithmetic and its role. We consider various rings for its performance
154 kb

#### THE THEOREMS OF CHEBYSHEV ABOUT THE DISTRIBUTION OF PRIME NUMBERS AND SOME PROBLEMS, CONNECTED WITH PRIME NUMBERS

abstract 1131509009 issue 113 pp. 115 – 126 30.11.2015 ru 1276
The article presents the theorem of Chebyshev on the distribution of primes, considering functions that approximated prime numbers. We have also considered a new function, which is quite good for approximation of prime numbers. A review of the known results on distribution of prime numbers is given as well
116 kb

#### ROOT POLYNOMIALS

abstract 0781204067 issue 78 pp. 842 – 851 30.04.2012 ru 1685
The article obtained the explicit form of root polynomials for cyclic polynomials of degree three over fields of characteristic 2. We also give an overview of known results on the root polynomials over arbitrary fields
395 kb 