Article Sidebar
Article Details
Open access articles published in the Journal of Agriculture, Science and Technology are under the terms of the Creative Commons Attribution (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited. The CC BY license permits commercial and non-commercial re-use of an open-access article, as long as the author is properly attributed.
Copyright on any research article published in the Journal of Agriculture, Science and Technology is retained by the author(s). The authors grant the Journal of Agriculture, Science and Technology with a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.
Use of the article in whole or in part in any medium requires proper citation as follows:
Title of Article, Names of the Author, Year of Publication, Journal Title, Volume (Issue) and page. Links to the final article on the JSRE website are encouraged.
The Creative Commons Attribution License does not affect any other rights held by authors or third parties in the article, including without limitation the rights of privacy and publicity. Use of the article must not assert or imply, whether implicitly or explicitly, any connection with, endorsement or sponsorship of such use by the author, publisher or any other party associated with the article.
For any reuse or distribution, users must include the copyright notice and make clear to others that the article is made available under a Creative Commons Attribution license, linking to the relevant Creative Commons web page. Users may impose no restrictions on the use of the article other than those imposed by the Creative Commons Attribution license.
To the fullest extent permitted by applicable law, the article is made available as is and without representation or warranties of any kind whether express, implied, statutory or otherwise and including, without limitation, warranties of title, merchantability, fitness for a particular purpose, non-infringement, absence of defects, accuracy, or the presence or absence of errors.
Main Article Content
Necessary conditions for existence of a friend of 38
Abstract
This paper sets out to, systematically, use properties of the abundancy index function to prove that a friend m of 38 must be an odd non-square multiple of 192 which is not divisible by 3, and that every prime factor q of m such that 4|(q + 1) has an even exponent in the prime factorization of m. In addition, if the power of 19 in m is 2, then 127|m in which case the power of 127 must be even, larger than 2 and not equal to 8, and if the power of 19 is 6, both 701 and 70841 would be compulsory prime factors of m, where the power of 701 cannot equal 1 or 3. The paper also establishes that it is not possible to have 8 as the power of 19 in the prime factorization of m.
Key words: Abundancy index, sum of divisors, friend, prime factor, power
