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Infinite Coprime Sequences

Published online by Cambridge University Press:  03 November 2016

A. W. F. Edwards
A. W. F. Edwards*
Affiliation:
Istituto di Genetica, University of Pavia, Italy
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Extract

1. Definition

We define an infinite coprime sequence as an infinite class of positive integers arranged in order of ascending magnitude, in which the highest common divisor of any two members is unity.

2. Note on prime numbers

If an infinite sequence of primes, constructed by some rule which does not invoke a knowledge of the sequence of primes, should ever be found, it will necessarily be an infinite coprime sequence. We thus concern ourselves in this note with the construction of infinite coprime sequences without using a knowledge of the sequence of primes.

Type
Research Article
Information
The Mathematical Gazette , Volume 48 , Issue 366 , December 1964 , pp. 416 - 422
Copyright
Copyright © Mathematical Association 1964

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