  We investigate the local integrability and linearizability of three
dimensional Lotka-Volterra equations at the origin. Necessary and sufficient
conditions for both integrability and linearizability are obtained for
(1,-1,1), (2,-1,1) and (1,-2,1)-resonance. To prove sufficiency, we mainly use
the method of Darboux with extensions for inverse Jacobi multipliers, and the
linearizability of a node in two variables with power-series arguments in the
third variable.
