ON THE $P_1$ PROPERTY OF SEQUENCES OF POSITIVE INTEGERS

Authors

  • T.L. Hakobyan Chair of Algebra and Geometry, YSU, Armenia

DOI:

https://doi.org/10.46991/PSYU:A/2016.50.2.022

Keywords:

Fermat’s number, prime number, greatest common divisor, Chinese Remainder Theorem

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≠1.

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Published

2016-06-06

How to Cite

Hakobyan, T. (2016). ON THE $P_1$ PROPERTY OF SEQUENCES OF POSITIVE INTEGERS. Proceedings of the YSU A: Physical and Mathematical Sciences, 50(2 (240), 22–27. https://doi.org/10.46991/PSYU:A/2016.50.2.022

Issue

Section

Mathematics