This final project discusses the increases of the sequence ⌊k √ n⌋ for any fixed positive integer k. For the increases of the sequence, the simplified expressions value of n (mod k) is given. This is a review of some parts of Hyatt and Skayers [Journal of Combinatorial Number Theory, 15 (2015), 1-12]. Furthermore, we provide the difference between the upper bound and lower bound of …