Extension of the Equation $\sum _{j=1}^{k}j{F}_j^p=F_n^q$ to a Family of Lucas Sequences

Benjamin Earp-Lynch, Simon Earp-Lynch, Omar Kihel +1

We solve the equation $\sum _{j=1}^{k}j{U}_j(x,y{)}^p=U_n(x,y{)}^q$ positive integers $x,p,q,k,n$, with $y=\pm 1$ and $\max \{p,q\}\le 11$, where $U_{m}(x,y)=\frac{α^{m}-β^…