Signature (Recurrence Relation)
Let a sequence be defined by
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Also define the associated Polynomial
and let
be its discriminant. The Perrin Sequence is a special case corresponding to 
. Thesignature 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 
, 
, 
,and 
. - 3. An Integer has an I-signature if its signature (mod ) is Congruent to(
), where 
and 
.
References
Adams, W. and Shanks, D. ``Strong Primality Tests that Are Not Sufficient.'' Math. Comput. 39, 255-300, 1982. Grantham, J. ``Frobenius Pseudoprimes.'' http://www.clark.net/pub/grantham/pseudo/pseudo1.ps.
- Jerabek's Hyperbola
- Jerk
- j-Function
- Jinc Function
- j-Invariant
- Jitter
- Joachimsthal's Equation
- Johnson Circle
- Johnson's Equation
- Johnson Solid
- Johnson's Theorem
- Join (Graph)
- Join (Spaces)
- Joint Distribution Function
- Joint Probability Density Function
- Joint Theorem
- Jonah Formula
- Jones Polynomial
- Jonquière's Function
- Jordan Algebra
- Jordan Curve
- Jordan Curve Theorem
- Jordan Decomposition Theorem
- Jordan-Hölder Theorem
- Jordan Measure