2020/09/24 by Zafer Şi̇ar, Şiar, Zafer, Refık Keskin +1
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Advanced Mathematical Theories and Applications #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2009.13387
Let k≥ 2 and let (Pn(k))n≥ 2-k be k-generalized Pell sequence defined by Pn(k)=2Pn-1(k)+Pn-2(k)+...+Pn-k(k) for n≥ 2 with initial conditions P-(k-2)(k)=P-(k-3)(k)=⋅ ⋅ ⋅ =P-1(k)=P0(k)=0,P1(k)=1. In this paper, we deal with the Diophantine equation Pn(k)=d( \frac10m-19) in positive integers n,m,k,d with k≥ 2, m≥ 2 and 1≤ d≤ 9. We will show that repdigits with at least two digits in the sequence ( Pn(k))n≥ 2-k are the numbers P5(3)=33 and P6(4)=88.