What was found
DURING CLIMBOUT, THE RIGHT FUEL BOOST PUMP CAUTION LIGHT ILLUMINATED. RAN CHECKLIST AND RESET THE RIGHT BOOST PUMP. WHEN THE PUMP WAS RESET, RIGHT LOW FUEL PRESSURE MASTER CAUTION ILLUMINATE, FOLLOWED BY THE RIGHT FUEL BOOST PUMP LIGHT. RAN THE CHECKLIST FOR LOW FUEL PRESSURE. NOTICED THE RIGHT N1 AND N2 INTERMITTENTLY SURGING 1-2 PERCENT. DIVERTED. DURING DESCENT BELOW 20,000 FEET, FELT A YAW AND NOTICED THE RIGHT ENGINE N1 AND ITT AT THE MAX RED LINE. PERFORMED RIGHT ENGINE SHUTDOWN AND THEN RAN THE ENGINE FAILURE. DECLARED AN EMERGENCY. SINGLE ENGINE LANDING WAS UNEVENTFUL. MAINTENANCE REMOVED AND REPLACED THE RIGHT ENGINE. AIRCRAFT WAS RETURNED TO SERVICE.