"The diophantine equation (k,m,n),
x_1^k + x_2^k + ... + x_m^k = y_1^k + y_2^k + ... + y_n^k
has no integral solution for k > m+n other than the trivial case when all x_i = y_i."
The author of this website is assuming that the question of whether the fourth case of EEC, for m+n = 4, or,
a^k+b^k = c^k+d^k; or a^k+b^k+c^k = d^k
has no solutions for all k > 4 will be settled for the first few exponents within the next decade or so. (Is for all exponents too much to ask?) In anticipation of that day, this timeline of EEC supplemented with interesting incidental details was created. This conjecture has a very good pedigree, with familiar names working on it some time or the other, and with no less than Euler himself providing the initial generalization.
Note: I'll be updating this timeline as needed. One good thing about this is that unlike FLT which has been settled, EEC is definitely still a work in progress.
