No label defined (Q6574110)

The gibonacci polynomials, \( g_n(x) \) are defined by the second-order recurrence relation: \( g_{n+2}(x)=xg_{n+1}(x)+g_n(x) \), where \( x \) is an arbitraty integer variable, \( g_0(x) \) and \( g_1(x) \) are arbitrary integer polynomials, and \( n\ge 0 \). In the paper under review, the authors use elementary number theory techniques to give formulas for infinite sums involving even (odd, respectively) powers of the gibonacci polynomials, unifying and extending some recent results on infinite sums involving low powers of the gibonacci polynomials.