TITLE: Is there a name for this Fibonacci Identity
QUESTION [9 upvotes]: Last night I was trying to solve a problem and discovered an identity relating to the Fibonacci sequence
$$ \left\lvert F_{i-j}F_{i+j} - F_{i-k}F_{i+k} \right\lvert = \left\lvert F_{k - j}F_{k+j} \right\lvert $$
Where $F_{n}$ is the $n$th term of the Fibonacci sequence. The modulus brackets remove the awkwardness of the $(-1)$ exponent, which gives
$$ F_{i-j}F_{i+j} - F_{i-k}F_{i+k} = F_{k-j}F_{j+k} (-1)^{(i + k)} $$
When $j=1$ and $k=0$ we get the Cassini identity, but is there a name for this more generalized form?

REPLY [2 votes]: This is equivalent to an identity of Alberto Tagiuri: equation (3) in 
Di alcune successioni ricorrenti a termini interi e positivi, Periodico di Matematica 16 (1900–1901), 1–12.