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1. A property of the set of primes as a multiplicative basis of the natural numbers.

Author

Karatsuba, A. A.

Subjects
*RINGS of integers, *FACTOR tables, *PRIME numbers, *NATURAL numbers, *LARGE cardinals (Mathematics), *SET theory, *MATHEMATICS
Abstract

The article focuses on a property of positive integers depicting the interpedendence between their construction and the form of their prime factors as established by E. A. Karatsuba and M. E. Changa. Karatsuba has discovered that the deviation of the cardinalities of sets of numbers with an odd and an even number of prime factors has the tendency to reach infinity under certain conditions on the factors. It presents several theorems which constitute the distribution of positive integers whose prime factors belong to certain subsets.

Published
2011
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