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
Famous quotes containing the word definition:
“According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.”
—Ana Castillo (b. 1953)
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)