New integer factorizations

Author:
Thorkil Naur

Journal:
Math. Comp. **41** (1983), 687-695

MSC:
Primary 11Y05

DOI:
https://doi.org/10.1090/S0025-5718-1983-0717713-2

MathSciNet review:
717713

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Abstract | References | Similar Articles | Additional Information

Abstract: New factorizations of Fibonacci numbers, Lucas numbers, and numbers of the form are presented together with the strategy (a combination of known factorization methods) used to obtain them.

**[1]**R. P. Brent, "An improved Monte Carlo factorization algorithm,"*BIT*, v. 20, 1980, pp. 176-184. MR**583032 (82a:10007)****[2]**R. P. Brent & J. M. Pollard, "Factorization of the eighth Fermat number,"*Math. Comp.*, v. 36, 1981, pp. 627-630. MR**606520 (83h:10014)****[3]**J. Brillhart, D. H. Lehmer & J. L. Selfridge, "New primality criteria and factorizations of ,"*Math. Comp.*, v. 29, 1975, pp. 620-647. MR**0384673 (52:5546)****[4]**D. Jarden,*Recurring Sequences*, 3rd ed., Riveon Lemathematica, Jerusalem, 1973.**[5]**D. H. Lehmer, Letter of July 14, 1982.**[6]**M. A. Morrison & J. Brillhart, "A method of factoring and the factorization of ,"*Math. Comp.*, v. 29, 1975, pp. 183-205. MR**0371800 (51:8017)****[7]**T. Naur,*Integer Factorization*, DAIMI PB-144, Dept. of Computer Science, University of Aarhus, Denmark, 1982.**[8]**J. M. Pollard, "Theorems on factorization and primality testing,"*Proc. Cambridge Philos. Soc.*, v. 76, 1974, pp. 521-528. MR**0354514 (50:6992)****[9]**J. M. Pollard, "A Monte Carlo method for factorization,"*BIT*, v. 15, 1975, pp. 331-334. MR**0392798 (52:13611)****[10]**J. M. Pollard, Letter of July 27, 1982.**[11]**B. D. Shriver & P. Kornerup,*A Description of the MATHILDA Processor*, DAIMI PB-52, Dept. of Computer Science, University of Aarhus, Denmark, 1975.**[12]**S. S. Wagstaff, Letters of July 20 and 26, 1982.**[13]**H. C. Williams, "A method of factoring,"*Math. Comp.*, v. 39, 1982, pp. 225-234. MR**658227 (83h:10016)****[14]**H. C. Williams & R. Holte, "Some observations on primality testing,"*Math. Comp.*, v. 32, 1978, pp. 905-917. MR**0476625 (57:16184)****[15]**H. C. Williams & J. S. Judd, "Determination of the primality of*N*by using factors of ,"*Math. Comp.*, v. 30, 1976, pp. 157-172. MR**0396390 (53:257)****[16]**H. C. Williams & J. S. Judd, "Some algorithms for prime testing using generalized Lehmer functions,"*Math. Comp.*, v. 30, 1976, pp. 867-886. MR**0414473 (54:2574)****[17]**H. C. Williams & F. Seah, "Some primes of the form ,"*Math. Comp.*, v. 33, 1979, pp. 1337-1342. MR**537980 (80g:10014)****[18]**M. C. Wunderlich & J. L. Selfridge, "A design for a number theory package with an optimized trial division routine,"*Comm. ACM.*, v. 17, 1974, pp. 272-276.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1983-0717713-2

Article copyright:
© Copyright 1983
American Mathematical Society