Application Of Euler’s Phi-Function In Abstract Algebra

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2014-09-24
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Euler’s phi – function ϕ(n) is defined for every positive integer n as follows: ϕ(1)=1 and whenn≥2then ϕ(n) is the number of distinct integers k∈{1,2,…,n-1}such that k and n are relatively prime. This thesis seeks to examine the application of Euler’s phi-function in the study of cyclic groups, field extensions and cyclotomic polynomials of a finite field. Euler’s phi – function ϕ(n) is defined for every positive integer n as follows: ϕ(1)=1 and whenn≥2then ϕ(n) is the number of distinct integers k∈{1,2,…,n-1}such that k and n are relatively prime. This thesis seeks to examine the application of Euler’s phi-function in the study of cyclic groups, field extensions and cyclotomic polynomials of a finite field.
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A Thesis Submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in Partial Fulfillment of the Degree of Master of Philosophy in Pure Mathematics, April-2014
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