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Vol 36 Iss. 3
Pages:
5-12
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RUS
Article

On the simplicity defect of a natural number

Authors:
M. L. Verzhbinskii
Date submitted:
1957-09-13
Date accepted:
1957-11-18
Date published:
1958-03-07

Abstract

In the present paper we study elementary properties of the number-theoretic function x (n) introduced by us.The function x (n) (defined below) is related to the variational treatment of various problems of additive number theory. With the help of x (n) we construct inequalities which are satisfied for the whole set M of rational positive integers, but turn into equalities for some subsets of the set M. Thus the extreme attribution of prime numbers, prime pairs, etc. is carried out.

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