NECESSARY CONDITIONS FOR EXISTENCE OF A FRIEND OF 38

dc.contributor.author	Gachimu, R. K.
dc.contributor.author	Mwathi, C. W.
dc.contributor.author	Kamuti, I. N.
dc.date.accessioned	2017-01-18T12:05:25Z
dc.date.available	2017-01-18T12:05:25Z
dc.date.issued	2017-01-18
dc.identifier.issn	1561-7645
dc.identifier.uri	http://journals.jkuat.ac.ke/index.php/jagst/index
dc.identifier.uri	http://hdl.handle.net/123456789/2523
dc.description.abstract	This paper sets out to, systematically, use properties of the abundancy index function to prove that a friend 􀝉 of 38 must be an odd non-square multiple of 19􀬶 which is not divisible by 3, and that every prime factor 􀝍 of 􀝉 such that 4\|(􀝍 + 1) has an even exponent in the prime factorization of 􀝉. In addition, if the power of 19 in 􀝉 is 2, then 127\|􀝉 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 􀝉, 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 􀝉.	en_US
dc.language.iso	en	en_US
dc.publisher	Journal of Agricultural Science and Technology, JKUAT	en_US
dc.relation.ispartofseries	Journal of Agricultural Science and Technology(JAGST);Vol. 14(1) 2012 38
dc.subject	Abundancy index	en_US
dc.subject	sum of divisors	en_US
dc.subject	friend	en_US
dc.subject	prime factor	en_US
dc.subject	power	en_US
dc.title	NECESSARY CONDITIONS FOR EXISTENCE OF A FRIEND OF 38	en_US
dc.type	Article	en_US