Aurifeuillean Factorization
المؤلف:
Riesel, H.
المصدر:
"Aurifeullian Factorization" in Appendix 6. Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser,
الجزء والصفحة:
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9-9-2020
1183
Aurifeuillean Factorization
A factorization of the form
 |
(1)
|
The factorization for 
was discovered by Aurifeuille, and the general form was subsequently discovered by Lucas. The large factors are sometimes written as 
and 
as follows:
which can be written
where 
and
REFERENCES:
Brillhart, J.; Lehmer, D. H.; Selfridge, J.; Wagstaff, S. S. Jr.; and Tuckerman, B. Factorizations of b-n+/-1, b=2, 3, 5, 6, 7, 10, 11, 12 Up to High Powers, rev. ed. Providence, RI: Amer. Math. Soc., pp. lxviii-lxxii, 1988.
Riesel, H. "Aurifeullian Factorization" in Appendix 6. Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser, pp. 309-315, 1994.
Wagstaff, S. S. Jr. "Aurifeullian Factorizations and the Period of the Bell Numbers Modulo a Prime." Math. Comput. 65, 383-391, 1996.
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