What was found
DISCREPANCY: LP 43593 - AIRCRAFT ENCOUNTERED A FAULT IN THE RIGHT FLIGHT MANAGEMENT COMPUTER (FMC). SIMULTANEOUSLY WITH THIS FAULT, AN AUTO-PILOT (A/P) CAUTION ILLUMINATED WITH AN UNCOMMANDED "NOSE DOWN" PITCH IN THE AIRCRAFT WITH THE A/P ENGAGED. IMMEDIATE ACTIONS: A/P WAS DISCONNECTED AND NOSE DOWN CONDITION CORRECTED. NO FURTHER ISSUES DURING THE REMAINDER OF THE FLIGHT. CORRECTIVE ACTION: THE RIGHT FMC WAS REPLACED WITH OPS CHECK NORMAL, AND THE A/P SYSTEM WAS WAS FUNCTIONALLY TESTED THROUGH ALL PARAMETERS WITH NO ISSUES NOTED.