Simson Identity of Generalized m-step Fibonacci Numbers

2019/03/04 by Soykan, Yüksel
#11B39 #11B83 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1903.01313

Abstract

One of the best known and oldest identities for the Fibonacci sequence F_n is F_n+1F_n-1-F_n²=(-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.

Related

• Linear Properties of Generalized n-step Fibonacci Numbers
• General convolution sums involving Fibonacci m-step numbers
• Generalized Fibonacci sequences and their properties
• Four New Generalized Fibonacci Number Summation Identities
• Cassini, d'Ocagne, and Vajda identities for n-step Fibonacci numbers