(untitled) (Journal of Mathematical Study, 2022)
In this paper, we find all repdigits expressible as difference of two Fibonacci numbers in base b for 2≤ b≤10. The largest repdigits in base b, which can be written as difference of two Fibonacci numbers are align*&F_9-F_4=34-3=31=(11111)_2, F_14-F_7=377-13=364=(111111)_3, &F_14-F_7=377-13=364=(222)_4, F_9-F_4=34-3=31=(111)_5, &F_11-F_4=89-3=86=(222)_6, F_13-F_5=233-5=228=(444)_7, &F_10-F_2=55-1=54=(66)_8, F_14-F_7=377-13=364=(444)_9,align* and F_15-F_10=610-55=555=(555)_10. As a result, it is shown that the largest Fibonacci number which can be written as a sum of a repdigit and a Fibonacci number is F_15=610=555+55=555+F_10.