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Nonexistence of even Fibonacci pseudoprimes of the 1st kind. (English) Zbl 0779.11007

For an integer \(m\) \((\geq 1)\) let \(V_ n(m)\) be the generalized Lucas numbers defined by \(V_ n(m)=mV_{n-1}(m)+V_{n-2}(m)\), \(V_ 0(m)=2\) and \(V_ 1(m)=m\). A composite number \(n\) is called Fibonacci pseudoprime of the \(m\)th kind if \(V_ n(m)=m\pmod n\). In the case \(m=1\) the author proves the following theorem: “There do not exist even Fibonacci pseudoprimes of the 1st kind”.
Reviewer: P.Kiss (Eger)

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11B50 Sequences (mod \(m\))
11A07 Congruences; primitive roots; residue systems
11A51 Factorization; primality
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