Some Researches On The K-power Fibonacci Sequence

In this thesis, the lower-power (k≤3) Fibonacci linear identity is popularized to k-power ones, so it is sucessful to solve the problems on the rank of k-power Fibonacci matrix and k-power Fibonacci matrix determine by the method above, and we also get two inference-s. These results can be popularized further in the general Fibonacci sequence, and we also get the similar result.This thesis consists of three chapters.In chapter 1, the revelant prepared knowledges are given to proves the k-power continuous k+2 Fibonacci numbers have linear relationship and the concrete linear identity are also proved.In chapter 2, the k-power Fibonacci matrix's definition is given to proves the k-power Fibonacci matrix rank is k+1, when m,r≥k+1. so method defeine the k-power Fibonacci matrix determine, and proves the K-power Fibonacci matrix determine Dt(k,n,r)=0 when t≥k+2, so we get two inferences.Finally, in chapter 3, the results from the above two chapters is popularized in a kind of general Fibonacci sequence, and we also get the similar result.