On a Theorem of Abel

Author: Hou, Shui-Hung

Source: American Mathematical Monthly, Volume 116, Number 7, August-September 2009 , pp. 629-630(2)

Publisher: Mathematical Association of America

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Abstract:

In this note, we provide an elementary proof of a theorem of Abel, which states that if P(x) and Q(x) are two polynomials such that degQ = n ≥ 2 Q(x) has no multiple roots, and deg P ≥ n−2, then Σⁿ_i=1P(r_i)/Q(r_i)= 0, where r₁, K, r_n are the n distinct roots of Q(x).

Document Type: Short communication

DOI: http://dx.doi.org/10.4169/193009709X458591

Publication date: 2009-08-01

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American Mathematical Monthly publishes articles, notes, and other features about mathematics and the profession. AMM readers span a broad spectrum of mathematical interests, and include professional mathematicians as well as students of mathematics at all collegiate levels.
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