LUCAS PSEUDOPRIME

In mathematics, 'Lucas pseudoprimes' in number theory are defined in terms of Lucas sequences. Suppose that
:$U\_n(P,Q)\; =\; (a^n-b^n)/(a-b)$
is a Lucas sequence, and ''D'' is the discriminant for the sequence. If ''p'' is an odd prime number for which the Jacobi symbol
:$(D/p)\; =\; k$
e 0,
then ''p'' is a factor of ''U_p-k''. However, there are also composite numbers satisfying this condition. These numbers are called Lucas pseudoprimes, named by analogy with pseudoprimes.
In the specific case of the Fibonacci sequence, where ''D'' = 5, the first pseudoprimes are 323 and 377; (5/323) and (5/377) are both −1, the 324th Fibonacci number is a multiple of 323, and the 378th is a multiple of 377.