Abstract:
Let (L-n) be the sequence of Lucas numbers defined byL(0)= 2, L-1= 1, andL(n)=Ln-1+L(n-2)forn >= 2. Let 0 <= m <= nandb= 2,3,4,5,6,7,8,9.In this study, we show that ifL(m)L(n)is a repdigit in the baseband has at least two digits, then LmLn is an element of {3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 28, 36, 54, 121, 228}. Furthermore, it is shown that ifL(n)is a repdigit in the baseband has at least two digits, then (n, b) = (2,2),(3,3),(4,6),(4,2),(6,5),(6,8). Namely, L-2= 3 = (11)(2),L-3= 4 = (11)(3),L-4= 7 = (11)(6) and L-4= 7 = (111)(2),L-6= 18 = (33)(5),L-6= 18 = (22)(8).