As reported to the FAA. Reports are unverified, and codes are left as the FAA publishes them.
What was found
CRUISING AT FL 390 NR 1 ENGINE FLAMED OUT. DESCENDED TO FL310 AND ATTEMPTED RESTART. N3 ROTATION WAS INDICATED. ENGINE DID NOT START. FLIGHT DIVERTED TO RBR AND LANDED WITHOUT INCIDENT. TROUBLESHOOTING NOTED GEARBOX FAILURE. REMOVED AND REPLACED NR 1 ENGINE GEARBOX AND FUEL PUMP. OPS CHECK NORMAL AS PER M/M 72-80-0 AND 28-20-0. NO LEAKS NOTED ON ENGINE RUN.