Some factorizations of $2^n \pm 1$ and related results
HTML articles powered by AMS MathViewer
- by John Brillhart and J. L. Selfridge PDF
- Math. Comp. 21 (1967), 87-96 Request permission
Corrigendum: Math. Comp. 21 (1967), 751.
References
- J. Brillhart, "Some miscellaneous factorizations," Math. Comp., v. 17, 1963, pp. 447– 450.
- John Brillhart, Concerning the numbers $2^{2p}+1$, $p$ prime, Math. Comp. 16 (1962), 424–430. MR 148593, DOI 10.1090/S0025-5718-1962-0148593-0 A. J. C. Cunningham & H. J. Woodall, Factorizations of $({y^n} \mp 1)$, Hodgson, London, 1925. E. Gabard, "Factorisation d’un nouveau nombre de Mersenne," Mathesis, 1959, p. 61.
- Dov Jarden, Divisibility of terms by their subscripts in sequences of sums of powers, Riveon Lematematika 12 (1958), 78–79 (Hebrew). MR 104618 M. Kraitchik, Recherches sur la Théorie des Nombres, Tome II, Paris, 1929.
- D. H. Lehmer, The Mechanical Combination of Linear Forms, Amer. Math. Monthly 35 (1928), no. 3, 114–121. MR 1521394, DOI 10.2307/2299504
- D. H. Lehmer, A Photo-Electric Number Sieve, Amer. Math. Monthly 40 (1933), no. 7, 401–406. MR 1522863, DOI 10.2307/2302134
- D. H. Lehmer, A machine for combining sets of linear congruences, Math. Ann. 109 (1934), no. 1, 661–667. MR 1512915, DOI 10.1007/BF01449160 D. H. Lehmer, "On the factorization of Lucas’ functions," Tôhoku Math. J., v. 34, 1931, pp. 1–7. D. H. Lehmer, "Tests for primality by the converse of Fermat’s theorem," Bull. Amer. Math. Soc., v. 33, 1927, pp. 327–340. D. H. Lehmer, "An extended theory of Lucas’ functions," Ann. of Math., v. 31, 1930, pp. 419–448.
- D. H. Lehmer, The primality of Ramanujan’s tau-function, Amer. Math. Monthly 72 (1965), no. 2, 15–18. MR 172855, DOI 10.2307/2313305 D. H. Lehmer, "On the converse of Fermat’s theorem," Amer. Math. Monthly, v. 43, 1936, pp. 347–354.
- Derrick Henry Lehmer, Guide to Tables in the Theory of Numbers, National Research Council, Washington, D.C., 1941. Bulletin of the National Research Council, No. 105. MR 0003625 D. N. Lehmer, "Hunting big game in the theory of numbers," Scripta Math., 1933, pp. 229–235.
- Raphael M. Robinson, The converse of Fermat’s theorem, Amer. Math. Monthly 64 (1957), 703–710. MR 98057, DOI 10.2307/2309747
- Raphael M. Robinson, Some factorizations of numbers of the form $2^{n}\pm 1$, Math. Tables Aids Comput. 11 (1957), 265–268. MR 94313, DOI 10.1090/S0025-5718-1957-0094313-6
- Daniel Shanks, Solved and unsolved problems in number theory. Vol. I, Spartan Books, Washington, D.C., 1962. MR 0160741 J. V. Uspensky & M. A. Heaslet, Elementary Number Theory, McGraw-Hill, New York, 1939, pp. 317–323. MR 1, 38.
Additional Information
- © Copyright 1967 American Mathematical Society
- Journal: Math. Comp. 21 (1967), 87-96
- DOI: https://doi.org/10.1090/S0025-5718-67-99898-5
- MathSciNet review: 0224532