New integer factorizations
Author:
Thorkil Naur
Journal:
Math. Comp. 41 (1983), 687695
MSC:
Primary 11Y05
MathSciNet review:
717713
Fulltext PDF Free Access
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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.
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 R. P. Brent, "An improved Monte Carlo factorization algorithm," BIT, v. 20, 1980, pp. 176184. MR 583032 (82a:10007)
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 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. 183205. MR 0371800 (51:8017)
 [7]
 T. Naur, Integer Factorization, DAIMI PB144, 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. 521528. MR 0354514 (50:6992)
 [9]
 J. M. Pollard, "A Monte Carlo method for factorization," BIT, v. 15, 1975, pp. 331334. 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 PB52, Dept. of Computer Science, University of Aarhus, Denmark, 1975.
 [12]
 S. S. Wagstaff, Letters of July 20 and 26, 1982.
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 H. C. Williams, "A method of factoring," Math. Comp., v. 39, 1982, pp. 225234. MR 658227 (83h:10016)
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 H. C. Williams & R. Holte, "Some observations on primality testing," Math. Comp., v. 32, 1978, pp. 905917. MR 0476625 (57:16184)
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 H. C. Williams & J. S. Judd, "Determination of the primality of N by using factors of ," Math. Comp., v. 30, 1976, pp. 157172. 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. 867886. MR 0414473 (54:2574)
 [17]
 H. C. Williams & F. Seah, "Some primes of the form ," Math. Comp., v. 33, 1979, pp. 13371342. 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. 272276.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198307177132
PII:
S 00255718(1983)07177132
Article copyright:
© Copyright 1983
American Mathematical Society
