Repdigits Base b as Difference of Two Fibonacci Numbers

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*}&F₉-F₄=34-3=31=(11111)₂,~~~~~~ F₁₄-F₇=377-13=364=(111111)₃,&F₁₄-F₇=377-13=364=(222)₄,~~ F₉-F₄=34-3=31=(111)₅,&F₁₁-F₄=89-3=86=(222)₆,~~~~~~~~ F₁₃-F₅=233-5=228=(444)₇,&F₁₀-F₂=55-1=54=(66)₈,~~~~~~~~~~ F₁₄-F₇=377-13=364=(444)₉,{align*} and F₁₅-F₁₀=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 F₁₅=610=555+55=555+F₁₀.