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Mathematics of Computation

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Note on irreducibility testing

Author: John Brillhart
Journal: Math. Comp. 35 (1980), 1379-1381
MSC: Primary 12-04; Secondary 10M05, 68C20
MathSciNet review: 583515
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Abstract: An effective method is developed for deducing the irreducibility of a given polynomial with integer coefficients from a single occurrence of a prime value of that polynomial.

References [Enhancements On Off] (What's this?)

    G. PÓLYA & G. SZEGÖ, Aufgaben und Lehrsätze aus der Analysis, Springer-Verlag, Berlin, 1964, b. 2, VIII, p. 127. J. V. USPENSKY, Theory of Equations, McGraw-Hill, New York, 1948.
  • John Brillhart, Michael Filaseta, and Andrew Odlyzko, On an irreducibility theorem of A. Cohn, Canadian J. Math. 33 (1981), no. 5, 1055–1059. MR 638365, DOI
  • D. K. Faddeev and I. S. Sominskii, Problems in higher algebra, W. H. Freeman and Co., San Francisco-London, 1965. Translated by J. L. Brenner. MR 0176990
  • A. L. CAUCHY, "Exercises de mathématiques," 1829 Oeuvres (2), v. 9, p. 122; Journ. École Poly., v. 25, 1837, p. 176.
  • Morris Marden, The Geometry of the Zeros of a Polynomial in a Complex Variable, Mathematical Surveys, No. 3, American Mathematical Society, New York, N. Y., 1949. MR 0031114

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Keywords: Irreducibility testing
Article copyright: © Copyright 1980 American Mathematical Society