Güney Duman, Merve;Öğüt, Ümmügülsüm;Keskin, Refik

Hokkaido Math. J.47, No. 3, 465-480 (2018).

Summary: Let \(P\geq 3\) be an integer. Let \((V_{n})\) denote generalized Lucas sequence defined by \(V_{0}=2\), \(V_{1}=P\), and \(V_{n+1}=PV_{n}-V_{n-1}\) for \(n\geq1\). In this study, when \(P\) is odd, we solve the equation \(V_{n}=wx^{2}\) for some values of \(w\). Moreover, when \(P\) is odd, we solve the equation \(V_{n}=wkx^{2}\) with \(k\mid P\) and \(k>1\) for \(w=3,11,13\). Lastly, we solve the equation \(V_{n}=wV_{m}x^{2}\) for \(w=7,11,13\).

Keywords:

generalized Lucas sequence;generalized Fibonacci sequence;congruence;square terms in Lucas sequences