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On the discriminator of Lucas sequences. (English. French summary) Zbl 1456.11021

In this work, the authors consider the Lucas sequences defined by \[ U_{n+2}(k)=(4k+2)U_{n+1}(k)-U_{n}(k) \] for \(n\geq 0\) with initial values \(U_{0}(k)=0\) and \(U_{1}(k)=1\), where \(k\geq 1\) is an integer. They defined the discriminator function \(\mathcal{D}_{k}(n)\) of the sequence \(U_{n}(k)\) to be the smallest integer \(m\) such that \(U_{0}(k),U_{1}(k),\cdots,U_{n-1}(k)\) are pairwise incongruent modulo \(m\). They derived some new results on \(\mathcal{D}_{k}(n)\).

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11B50 Sequences (mod \(m\))
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