Detecting prime numbers via roots of polynomials

• Autores: David E. Dobbs
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 43, Nº. 3, 2012, págs. 381-387
• Idioma: inglés
• DOI: 10.1080/0020739x.2011.582182
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• Resumen

  • It is proved that an integer n?=?2 is a prime (resp., composite) number if and only if there exists exactly one (resp., more than one) nth-degree monic polynomial fwith coefficients in Zn, the ring of integers modulo n, such that each element of Znis a root of f. This classroom note could find use in any introductory course on abstract algebra or elementary number theory.