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Journal Article

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
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Page Count: 3

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Topics: Integers, Rationality, Polynomials, Mathematical problems, Number theory
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Gauss's Lemma and the Irrationality of Roots, Revisited
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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.

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