Odd T > 1 is clearly impossible. For odd T, 2^T = -1 mod 3
(-1^T = -1 when T is odd.) But 3^U = 0 mod three for all U > 0, and
-1 mod 3 - 0 mod 3 can never = 1 (mod 3).
The exception here is that 3^0 = 1 mod 3, and so there can be a
solution when T is odd and U = 0 : which is one of the two solutions
given -- T=1,U=0.
I don't know if even T are subject to a similar treatment or not...
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Posted by Paul
on 2005-07-29 21:13:27 |
another small observation
