Vajda's Identity
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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.