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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Note on irreducibility testing
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by John Brillhart PDF
Math. Comp. 35 (1980), 1379-1381 Request permission


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.
    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 10.4153/CJM-1981-080-0
  • 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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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 35 (1980), 1379-1381
  • MSC: Primary 12-04; Secondary 10M05, 68C20
  • DOI:
  • MathSciNet review: 583515