where each x_y is a distinct integer.

(Or prove that it is impossible).

Since any X integer raised to the 4th power yields a positive number, X<=6 because X> 6 yields values higher than 1999.

So, -6<= X <=6, or we can use the X =1, to X=6 values twice and still have a distintive integer.

A quick check of these, and one can see that 2004 has distintive X solution, but not 1999.