Academic Journals Database
Disseminating quality controlled scientific knowledge

Integral Sequences of Infinite Length Whose Terms Are Relatively Prime

ADD TO MY LIST
 
Author(s): Kazuyuki Hatada

Journal: Advances in Pure Mathematics
ISSN 2160-0368

Volume: 03;
Issue: 01;
Start page: 24;
Date: 2013;
Original page

Keywords: Relatively Prime | Integral Sequences of Infinite Length | Sets of Infinitely Many Prime Numbers

ABSTRACT
It is given in Weil and Rosenlicht ([1], p. 15) that   (resp. 2) for all non-negative integers m and n with m≠n if c is any even (resp. odd) integer. In the present paper we generalize this. Our purpose is to give other integral sequences   such that G.C.D.(ym,yn)=1 for all positive integers m and n with m≠n. Roughly speaking we show the following 1) and 2). 1) There are infinitely many polynomial sequences   such that G.C.D.(fm(a),fn(a))=1 for all positive integers m and n with with m≠n and infinitely many rational integers a. 2) There are polynomial sequences   such that G.C.D.(gm(a,b),gn(a,b))=1 for all positive integers m and n with m≠n and arbitrary (rational or odd) integers a and b with G.C.D.(a,b)=1. Main results of the present paper are Theorems 1 and 2, and Corollaries 3, 4 and 5.

Tango Jona
Tangokurs Rapperswil-Jona

    
RPA Switzerland

Robotic Process Automation Switzerland