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On Lucas pseudoprimes of the form $$ax^2+bxy+cy^2$$ in arithmetic progression $$AX+B$$ with a prescribed value of the Jacobi symbol. (English) Zbl 1028.11008
Let $$F$$ be a binary indefinite integral quadratic form and assume it has odd fundamental discriminant $$d$$ and belongs to the principal genus. Consider the sequence of Lucas numbers with parameters $$P$$ and $$Q$$ and $$D= P^2-4Q$$. Then, under some natural conditions on $$P,Q,D,A,B$$, if the arithmetic progression $$AX+B$$ represents at all an odd integer $$n_0$$ with the Jacobi symbol $$(D/n_0)=\varepsilon$$, where $$\varepsilon = \pm 1$$ is fixed, then the progression represents infinitely many Lucas pseudoprimes $$n$$ with parameters $$P,Q$$, represented by the quadratic form $$F$$ and satisfying $$(D/n)=\varepsilon$$.
##### MSC:
 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 11A15 Power residues, reciprocity
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##### References:
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