Let a sequence be defined by
Also define the associated Polynomial
and let be its discriminant. The Perrin Sequence is a special case corresponding to . The
signature mod of an Integer with respect to the sequence is then defined as the 6-tuple (,
, , , , ) (mod ).
- 1. An Integer has an S-signature if its signature (mod ) is (, , , , ).
- 2. An Integer has a Q-signature if its signature (mod ) is Congruent to (
where, for some Integer with
- 3. An Integer has an I-signature if its signature (mod ) is Congruent to
See also Perrin Pseudoprime
Adams, W. and Shanks, D. ``Strong Primality Tests that Are Not Sufficient.'' Math. Comput. 39, 255-300, 1982.
Grantham, J. ``Frobenius Pseudoprimes.''
© 1996-9 Eric W. Weisstein