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Gauss's Lemma and the Irrationality of Roots, Revisited
Vol. 85, No. 2 (April 2012), pp. 114-116
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.85.2.114
Page Count: 3
You can always find the topics here!Topics: Integers, Rationality, Polynomials, Mathematical problems, Number theory
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Summary An idea of T. Estermann (1975) for demonstrating the irrationality of √2 is extended to obtain a conceptually simple proof of Gauss's Lemma, according to which real roots of monic polynomials with integer coefficients are either integers or irrational. The standard proof of the lemma is also reviewed.
Copyright the Mathematical Association of America 2012