When P and Q are integers such that D = P^2 - 4Q!=0, define the Lucas sequence {U_k} by U_k = (a^k - b^k)/(a - b) for k>=0, with a and b the two roots of x^2 - P x + Q = 0. Then define a Lucas pseudoprime as an odd composite number n such that n not vertical bar Q, the Jacobi symbol (D/n) = - 1, and n|U_(n + 1).

extra strong Lucas pseudoprime | Lucas number | Lucas sequence | pseudoprime | strong Lucas pseudoprime

PrimeQ

Édouard Lucas