>> X=[18 24; 24 32], Y=[16 -12; -12 9], Z=[34 12; 12 41]

X =

    18    24
    24    32


Y =

    16   -12
   -12     9


Z =

    34    12
    12    41

>> X^3 + Y^3

ans =

       55000       52500
       52500       85625

>> Z^3

ans =

       55000       52500
       52500       85625

So ...

Conjecture: If X, Y, and Z are integer symmetric matrices of the same order,
            and X^n + Y^n = Z^n for n > 2, then YZ or ZX or XY must be 0.

Francis Su, Math Dept., Harvey Mudd, visiting Cornell, has
shown this false with the example X = [ 4  3; 3 -3], Y = [-4  0; 0 -4], 
Z = [ 3  3; 3 -4]! So the question becomes:
what is the structure of counterexamples to the symmetric matrix
Fermat's last theorem?

Question: is this a "bad" question? (Do integer values make sense for
          symmetric matrices, where diagonalization over the reals is
          the big tool?)