FLC OF AN MDT SECURED 1 ENG AFTER IT QUIT DURING CRUISE; DECLARED AN EMER AND DIVERTED TO LAND.

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FLT DEN-GCC-SHR DEPARTED AT XH15. TEMPS WERE HIGH (ISA PLUS 10 TO PLUS 15) AND WE WERE HVY. CLB TO FL240 WAS SLOW; BUT WE DID IT ANYWAY TO GET ABOVE THE WX AND THE BUMPS. AT ONE POINT IN THE CLB THE CAPT; WHILE ATTEMPTING TO GET MORE PERFORMANCE; PUSHED THE PWR LEVERS UP A LITTLE TOO MUCH AND GOT A BRIEF TEMP CAUTION. HOWEVER; ENG LIMITS WERE NOT EXCEEDED. AFTER LEVELOFF; NW OF CYS; AFTER I HAD CONFIGURED FOR CRUISE PWR; I NOTICED THAT THE PROPS DID NOT SEEM TO BE SYNCHRONIZED. I TWICE ATTEMPTED TO SYNCHRONIZE THEM (INCLUDING TURNING OFF THE SYNCHROPHASER AND MANUALLY ADJUSTING THE CONDITION LEVERS) BUT NEVER SUCCEEDED IN GETTING THEM SYNCHRONIZED. ABOUT 5 MINS AFTER MY LAST ATTEMPT; THE ACFT YAWED; WE GOT A CAUTION ON THE ELECTRONIC CTL UNIT AND ON THE LLAS. THE ENG INSTS SHOWED THAT THE #2 ENG HAD QUIT RUNNING. WE PERFORMED THE IMMEDIATE ACTION ITEMS ON THE ENG FIRE/FAILURE CHKLIST AND IN ACCORDANCE WITH THE REMAINDER OF THE CHKLIST; SECURED THE #2 ENG. WE REQUESTED A DSCNT AND A HDG FOR CYS BECAUSE OF HAVING LOST AN ENG. WE WERE TOLD TO STAND BY. I; THE PF; ASKED THE CAPT TO INFORM CTR THAT WE WERE DSNDING AND THAT WE WERE MAKING DIRECT TO CYS. WE BOTH JUDGED CYS TO BE THE NEAREST SUITABLE ARPT IN POINT OF TIME BECAUSE OF WX 6000 FT; LNDG RWYS 8/26; GOOD CRASH/FIRE/RESCUE CAPABILITIES. WE DECLARED AN EMER. THE NEXT MORNING; AFTER MAINT HAD CLRED THE ACFT; WE FERRIED IT BACK TO DEN WITHOUT INCIDENT. MAINT SAID THEY WERE ABLE TO START #2 WITHOUT DOING ANY REPAIRS; BUT AS A PRECAUTION; THEY PUT IN A DIFFERENT ELECTRONIC CTL UNIT.