Vajda's Identity

Theorem

Let $F_n$ be the $n$th Fibonacci number.

Formulation 1

$F_{n + i} F_{n + j} - F_n F_{n + i + j} = \paren {-1}^n F_i F_j$

Formulation 2

$F_{n + k} F_{m - k} - F_n F_m = \left({-1}\right)^n F_{m - n - k} F_k$

Source of Name

This entry was named for Steven Vajda.