Some factorizations of and related results

Authors:
John Brillhart and J. L. Selfridge

Journal:
Math. Comp. **21** (1967), 87-96

DOI:
https://doi.org/10.1090/S0025-5718-67-99898-5

Corrigendum:
Math. Comp. **21** (1967), 751.

MathSciNet review:
0224532

Full-text PDF Free Access

References | Additional Information

**[1]**J. Brillhart, "Some miscellaneous factorizations,"*Math. Comp.*, v. 17, 1963, pp. 447- 450.**[2]**John Brillhart,*Concerning the numbers 2^{2𝑝}+1, 𝑝 prime*, Math. Comp.**16**(1962), 424–430. MR**0148593**, https://doi.org/10.1090/S0025-5718-1962-0148593-0**[3]**A. J. C. Cunningham & H. J. Woodall,*Factorizations of*, Hodgson, London, 1925.**[4]**E. Gabard, "Factorisation d'un nouveau nombre de Mersenne,"*Mathesis*, 1959, p. 61.**[5]**Dov Jarden,*Divisibility of terms by their subscripts in sequences of sums of powers*, Riveon Lematematika**12**(1958), 78–79 (Hebrew). MR**0104618****[6]**M. Kraitchik,*Recherches sur la Théorie des Nombres*, Tome II, Paris, 1929.**[7]**D. H. Lehmer,*The Mechanical Combination of Linear Forms*, Amer. Math. Monthly**35**(1928), no. 3, 114–121. MR**1521394**, https://doi.org/10.2307/2299504**[8]**D. H. Lehmer,*A Photo-Electric Number Sieve*, Amer. Math. Monthly**40**(1933), no. 7, 401–406. MR**1522863**, https://doi.org/10.2307/2302134**[9]**D. H. Lehmer,*A machine for combining sets of linear congruences*, Math. Ann.**109**(1934), no. 1, 661–667. MR**1512915**, https://doi.org/10.1007/BF01449160**[10]**D. H. Lehmer, "On the factorization of Lucas' functions,"*Tôhoku Math. J.*, v. 34, 1931, pp. 1-7.**[11]**D. H. Lehmer, "Tests for primality by the converse of Fermat's theorem,"*Bull. Amer. Math. Soc.*, v. 33, 1927, pp. 327-340.**[12]**D. H. Lehmer, "An extended theory of Lucas' functions,"*Ann. of Math.*, v. 31, 1930, pp. 419-448.**[13]**D. H. Lehmer,*The primality of Ramanujan’s tau-function*, Amer. Math. Monthly**72**(1965), no. 2, 15–18. MR**0172855**, https://doi.org/10.2307/2313305**[14]**D. H. Lehmer, "On the converse of Fermat's theorem,"*Amer. Math. Monthly*, v. 43, 1936, pp. 347-354.**[15]**Derrick Henry Lehmer,*Guide to Tables in the Theory of Numbers*, Bulletin of the National Research Council, no. 105, National Research Council, Washington, D. C., 1941. MR**0003625****[16]**D. N. Lehmer, "Hunting big game in the theory of numbers,"*Scripta Math.*, 1933, pp. 229-235.**[17]**Raphael M. Robinson,*The converse of Fermat’s theorem*, Amer. Math. Monthly**64**(1957), 703–710. MR**0098057**, https://doi.org/10.2307/2309747**[18]**Raphael M. Robinson,*Some factorizations of numbers of the form 2ⁿ±1*, Math. Tables Aids Comput.**11**(1957), 265–268. MR**0094313**, https://doi.org/10.1090/S0025-5718-1957-0094313-6**[19]**Daniel Shanks,*Solved and unsolved problems in number theory. Vol. I*, Spartan Books, Washington, D.C., 1962. MR**0160741****[20]**J. V. Uspensky & M. A. Heaslet,*Elementary Number Theory*, McGraw-Hill, New York, 1939, pp. 317-323. MR**1**, 38.

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-67-99898-5

Article copyright:
© Copyright 1967
American Mathematical Society