Aurifeuillean Factorization
A factorization of the form
 | (1) |
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 Wagstaff, S. S. Jr. ``Aurifeullian Factorizations and the Period of the Bell Numbers Modulo a Prime.'' Math. Comput. 65, 383-391, 1996.
, 
, 
Up to High Powers, rev. ed. Providence, RI: Amer. Math. Soc., pp. lxviii-lxxii, 1988.
- Diminished Rhombicosidodecahedron
- Dini Expansion
- Dini's Surface
- Dini's Test
- Dinitz Problem
- Diocles's Cissoid
- Diophantine Equation
- Diophantine Equation--10th Powers
- Diophantine Equation--5th Powers
- Diophantine Equation--6th Powers
- Diophantine Equation--7th Powers
- Diophantine Equation--8th Powers
- Diophantine Equation--9th Powers
- Diophantine Equation--Cubic
- Diophantine Equation--Linear
- Diophantine Equation nth Powers
- Diophantine Equation--Quadratic
- Diophantine Equation--Quartic
- Diophantine Quadruple
- Diophantine Set
- Diophantus Property
- Diophantus' Riddle
- Dipyramid
- Dirac Delta Function
- Dirac Matrices