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References
M.F. Atiyah, I.G. Macdonald, Introduction to commutative algebra, Addison-Wesley, Reading, Mass., 1969.
N. Bourbaki, Algèbre commutative, Chapitres 1 et 2, Hermann, Paris, 1961.
J. Brillhart, D.H. Lehmer, J.L. Selfridge, New primality criteria and factorizations of 2m±1, Math. Comp. 29 (1975), 620–647.
S.U. Chase, D.K. Harrison, A. Rosenberg, Galois theory and Galois cohomology of commutative rings, Memoirs Amer. Math. Soc. 52 (1965), 15–33.
H. Cohen, H.W. Lenstra, Jr., Primality testing and Jacobi sums, Math. Comp. 42 (1984), 297–330.
F. DeMeyer, E. Ingraham, Separable algebras over commutative rings, Lecture Notes in Math. 181, Springer-Verlag, Berlin, 1971.
J.D. Dixon, Factorization and primality tests, Amer. Math. Monthly 91 (1984), 333–352.
D.E. Knuth, The art of computer programming, vol. 2, Seminumerical algorithms, 2nd ed., Addison-Wesley, Reading, Mass., 1981.
A.K. Lenstra, Factorization of polynomials, pp. 169–198 in
H.W. Lenstra, Jr., Primality testing, pp. 55–77 in
H.W. Lenstra, Jr., Primality testing algorithms (after Adleman, Rumely and Williams), Sém. Bourbaki 33 (1980/1981), Exposé 576, pp. 243–257 in: Lecture Notes in Math. 901, Springer-Verlag, Berlin, 1981.
H.W. Lenstra, Jr., Primality testing with Artin symbols, pp. 341–347 in: N. Koblitz (ed.), Number theory related to Fermat’s last theorem, Progress in Mathematics 26, Birkhäuser, Boston, 1982.
H.W. Lenstra, Jr., R. Tijdeman (eds), Computational methods in number theory, Mathematical Centre Tracts 154/155, Mathematisch Centrum, Amsterdam, 1982.
H.C. Williams, Primality testing on a computer, Ars Combin. 5 (1978), 127–185.
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Lenstra, H.W. (1985). Galois theory and primality testing. In: Reiner, I., Roggenkamp, K.W. (eds) Orders and their Applications. Lecture Notes in Mathematics, vol 1142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074800
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DOI: https://doi.org/10.1007/BFb0074800
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