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The irreducible factorization of Fibonacci polynomials over \(\mathbb Q\). (English) Zbl 1009.11012

\(F_n(a,b)\) is defined by \(y_0=0\), \(y_1=1\), \(y_{n+1}= ay_n+ by_{n-1}\), \(n\geq 1\). Then \(F_n(x,1)= U_n(x)\) are the Fibonacci polynomials, and the main result of the paper is the prime factorization of \(U_n(x)\) over the field of rational numbers.

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11B83 Special sequences and polynomials
12E05 Polynomials in general fields (irreducibility, etc.)
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