“Aurifeuillean Factorization”的概念、定义、习题解题方法及翻译-数学辞典

单词

Aurifeuillean Factorization

释义

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

			(2)

			(3)

which can be written

			(4)
			(5)
			(6)

where

and

			(7)
			(8)
			(9)

See also Gauss's Formula

References

Brillhart, J.; Lehmer, D. H.; Selfridge, J.; Wagstaff, S. S. Jr.; and Tuckerman, B. Factorizations of , , Up to High Powers, rev. ed. Providence, RI: Amer. Math. Soc., pp. lxviii-lxxii, 1988.

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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