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 re: only one by Charlie)

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

 Correct!!

t^2+t+1=0

t^2+t=-1=6 mod 7

 t*( t+1)=6

t=2  or t=4

This is how I have missed  50% of solutions  

Ady

Posted by Ady TZIDON on 2008-10-07 14:17:30