English

Simson Identity of Generalized m-step Fibonacci Numbers

Number Theory 2019-03-05 v1

Abstract

One of the best known and oldest identities for the Fibonacci sequence FnF_n is Fn+1Fn1Fn2=(1)nF_{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.

Cite

@article{arxiv.1903.01313,
  title  = {Simson Identity of Generalized m-step Fibonacci Numbers},
  author = {Yüksel Soykan},
  journal= {arXiv preprint arXiv:1903.01313},
  year   = {2019}
}
R2 v1 2026-06-23T07:57:38.624Z