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.

(In reply to only one by Ady TZIDON)

T need not be 2 mod 7 in order for T^2 + T + 1 to be a multiple of 7.

T mod 7     T^2 + T + 1  mod 7

0                      1
1                      3
2                      0
3                      6
4                      0
5                      3
6                      1

Posted by Charlie on 2008-10-07 13:13:20