I don't actually know that, although I imagine it's quite well studied and not so tricky to figure out after a bit of work. See if you can do it under the 'finite elements' interpretation, where you literally don't worry about what the Fibonacci number is in the integers, but just what it is in terms of the symbols 0, 1, ... , 8. In fact by writing that I just figured it out, it's quite easy given what I tried to explain above. See if you can get it.

PM me your email address and I'll send you the document. The relevant bit starts at section 4.1. But I really recommend reading it all the way through (except maybe section 3 first time), it's a perfect introduction to what it's like on a university maths course (it's from a first term lecture series), the pure half anyway; and you need literally zero prior knowledge, but once you're done you'll know more number theory than your average mathematics graduate. The stuff in section 6 is still probably the coolest thing I have seen in my degree, it's about the different sizes of infinity.