A note on strong Dickson pseudoprimes (Q1277247)

The well-known Lucas sequences \(U_k\), \(V_k\) give rise to various kinds of pseudo-primes. For example, strong \(Q\)-Dickson pseudoprimes (sDpsp\((Q)\)) are composite integers \(n>2\) satisfying \(V_n(P,Q)\equiv P\pmod n\) for all \(P\in \mathbb{Z}\). Superstrong Dickson pseudoprimes (ssDpsp) are sDpsp\((Q)\) for all possible parameters \(Q\). The paper focusses mainly on both types of pseudoprimes. In particular, methods are indicated to construct sDpsp\((Q)\), above all for \(Q=1\). Also, criteria are derived for an sDpsp(1) to be ssDpsp. Finally, the occurrence of ssDpsp's in other series of pseudoprimes is investigated.