Simson Identity of Generalized m-step Fibonacci Numbers

One of the best known and oldest identities for the Fibonacci sequence $F_n$ is $F_{n+1}{F}_{n-1}-F_n^2=(-1{)}^n$ which was derived first by R. Simson in 1753 and it is now called as Simson or Cassini Identity. In this paper, we generalize this result to generalized m-step Fibonacci numbers and give an attractive formula. Furthermore, we present some Simson’s identities of particular generalized m-step Fibonacci sequences.