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Getting the bases with aabbcc (Posted on 20081007) 

Determine all possible positive integer base(s) T such that:
(111)_{T} = (aabbcc)_{6}, where each of a, b and c denotes a different base 6 digit from 0 to 5 and, a is not zero.
Note: Try to solve this problem analytically, although computer program/ spreadsheet solutions are welcome.
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