Mathematics

On the $P_1$ property of sequences of positive integers

T. L. Hakobyan

Chair of Algebra and Geometry YSU, Armenia

Abstract: In this paper we introduce the concept of $P_1$ property of sequences, consisting of positive integers and prove two criteria revealing this property. First one deals with rather slow increasing sequences while the second one works for those sequences of positive integers which satisfy certain number theoretic condition. Additionally, we prove the unboundedness of common divisors of distinct terms of sequences of the form $(2^{2^n}+d)^{\infty}_{n=1}$ for integers $d\neq1.$

Keywords: Fermat's number, prime number, greatest common divisor, Chinese Remainder Theorem.

MSC: Primary 11A00; Secondary 11A05, 11A41, 11A51

Received: 16.03.2016
Accepted: 29.04.2016

Language: English