Matteo Beccuti

Frobenius Classification of Somer's Five Semiprime Lucas Pseudoprime Types

Let U(P,Q) be a Lucas sequence with discriminant D = P² − 4Q. Somer identified five semiprime families N = pq of Lucas pseudoprimes, with q = p + 2, 2p − 3, 2p − 1, 2p + 1, or 2p + 3, under prescribed quadratic-character conditions. We determine exactly which members of these fiv...

Frobenius Classification of Somer's Five Semiprime Lucas Pseudoprime Types

Let U(P,Q) be a Lucas sequence with discriminant D = P² − 4Q. Somer identified five semiprime families N = pq of Lucas pseudoprimes, with q = p + 2, 2p − 3, 2p − 1, 2p + 1, or 2p + 3, under prescribed quadratic-character conditions. We determine exactly which members of these fiv...

A Frobenius Trichotomy for Rotkiewicz's Semiprime Fibonacci Pseudoprime Families

Rotkiewicz characterized three semiprime families of Fibonacci pseudoprimes: p(p+2), p(2p−1), and p(2p+3), under explicit congruence conditions on the prime p. We determine exactly which members of these families satisfy the stronger Frobenius–Fibonacci pseudoprime conditions. If...