Gauss's Lemma and the irrationality of roots, revisited

Research output: Contribution to journalReview articlepeer-review


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.

Original languageEnglish
Pages (from-to)114-116
Number of pages3
JournalMathematics Magazine
Issue number2
StatePublished - 2012


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