Is this a bountied low-quality question? The remarks in the comments and answers prove that the question is non-trivial, but that doesn't make up for the lack of context?
I'm not sure if this is a good or bad question, but I think it may benifit from moving to a different SE site. (Sorry if this is outside of the wheelhose of CURED, but I don't know if there is a chat room for migrate sudgestions)
@Peter Definitely, we'll let it hang around and close later, or we can flag immediately. What I've usually seen is that if the number (in this case 29 +\sqrt(21)) isn't a Pisot number (or a conjugate of one) then this kind of a question is best solved using a computer and/or finding modular patterns of very short period, which isn't the case as one answer evidences.