COMMON TERMS k-GENERALIZED FIBONACCI AND LUCAS SEQUENCES

Let (F_n^((k))) and (L_n) be the k-generalized Fibonacci and Lucas sequences. In this study, we find k-generalized Fibonacci numbers which are Lucas numbers. Namely, we tackle the Diophantine equation F_n^((k))=L_m, in non-negative integers k,n,m with k≥3. Solutions to this equation can be expressed as F_3^((k))=L_0=2,F_1^((k))=L_1=1,F_4^((k))=L_3=4,F_5^((3))=L_4=7,and F_7^((4))=L_7=29.