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In mathematics, in particular number theory, an odd composite number N is a Somer–Lucas d-pseudoprime if there exists a nondegenerate Lucas sequence U {\displaystyle U} with the discriminant D = P 2 − 4 Q , {\displaystyle D=P^{2}-4Q,} such that gcd = 1 {\displaystyle \gcd=1} and the rank appearance of N in the sequence U is
where {\displaystyle \left} is the Jacobi symbol.
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