Definition
Given two integer parameters P and Q which satisfy
the Lucas sequences of the first and second kind, Un(P,Q) and Vn(P,Q) respectively, are defined by the recurrence relations
and
We can write
where a and b are roots of the auxiliary polynomial X2 - P X + Q, of discriminant D.
If p is an odd prime number then
- Vp is congruent to P modulo p.
and if the Jacobi symbol
- ,
then p is a factor of Up-ε.
Read more about this topic: Lucas Pseudoprime
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