Irreducibility of $x^n-a$
Biswajit Koley, A.Satyanarayana Reddy
TL;DR
This paper provides an elementary proof for Capelli's criterion on when the polynomial x^n - a is reducible over the rationals, simplifying the understanding of its algebraic properties.
Contribution
It offers a new, elementary proof of Capelli's necessary and sufficient condition for reducibility of x^n - a over ield, enhancing accessibility and comprehension.
Findings
Elementary proof of Capelli's criterion
Clarification of reducibility conditions for x^n - a
Simplified approach to polynomial reducibility
Abstract
A. Capelli gave a necessary and sufficient condition for the reducibility of over . In this article, we are providing an alternate elementary proof for the same.
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Taxonomy
TopicsMathematics and Applications · Advanced Combinatorial Mathematics · graph theory and CDMA systems