Original: Three suppliers provide turbofan engines for the A320 series: CFM International with their CFM56, International Aero Engines, offering the V2500 and Pratt & Whitney whose PW6000 engines are only available for the A318 variant.
Simplified: Engines The A319, A320 and A321 have engines made by two different companies; International Aero Engines (IAE) supply the V2500 and CFM International provide the CFM56.