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Gauss's Lemma and the Irrationality of Roots, Revisited

David Gilat
Mathematics Magazine
Vol. 85, No. 2 (April 2012), pp. 114-116
DOI: 10.4169/math.mag.85.2.114
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.85.2.114
Page Count: 3
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Gauss's Lemma and the Irrationality of Roots, Revisited
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Abstract

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.

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