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Is Cellular One a legacy GSM or CDMA carrier. If it's the latter, then only a Verizon iPhone 5S will work. Apple started activating the CDMA radios in all unlocked iPhones with the iPhone 6 and 6 Plus last year.
 
I don't know the answer to that question. I have an unlocked 5s that a friend on Cellular One wants, but sounds like it won't work.
 
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