Abstract: In this paper, we derive some algebraic identities on
right and left neighbors R(F) and L(F) of an indefinite binary
quadratic form F = F(x, y) = ax2 + bxy + cy2 of discriminant
Δ = b2 -4ac. We prove that the proper cycle of F can be given by
using its consecutive left neighbors. Also we construct a connection
between right and left neighbors of F.