## 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)

Wagstaff, S. S. Jr. Aurifeullian Factorizations and the Period of the Bell Numbers Modulo a Prime.'' Math. Comput. 65, 383-391, 1996.