So a common method used to construct non-zero $\omega$-REA arithmetic degrees with various properties is to build an $\omega$-REA operator $J$ satisfying the constraints that (for all $X$) $$\tag{1} J(X') \equiv_T J(X) \oplus X'$$ $$\tag{2} J(X) >_T X$$ Inductively, 1 implies that $J(X^n) \equiv_...

I'm looking for a nontrivial, but not super difficult question concerning Fibonacci numbers. It should be at a level suitable for an undergraduate course. Here is a (not so good) example of the sort of thing I am looking for. a) Prove that every positive integer can be represented in binary o...