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It depends on rather you are jailbroken or not. If you are jailbroke then you can buy two apps displayout and resupported 4 and then any one will work. I personally bought a cable for 99 cent and it works great. But if you are not jailbroke then I would recommend the apple's cable Right now Radio Shack has them for 30 dollars.
 
It will definitely charge the phone. I use that function all the time. I've only had it connected to the TV, so I don't know if you can use it to sync, but I doubt it.
 
I know the Apple one will sync and charge the iDevice. I use it all the time in place of the regular sync cable.
 
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