## Fermat's theorem math problem

from: http://www.math.utah.edu/~cherk/puzzles.html
 Fermat, computers, and a smart boy A computer scientist claims that he proved somehow that the Fermat theorem is correct for the following 3 numbers: x=2233445566, y=7788990011, z=9988776655 He announces these 3 numbers and calls for a press conference where he is going to present the value of N (to show that x^N + y^N = z^N and that the guy from Princeton was wrong). As the press conference starts, a 10-years old boy raises his hand and says that the respectable scientist has made a mistake and the Fermat theorem cannot hold for those 3 numbers. The scientist checks his computer calculations and finds a bug. How did the boy figure out that the scientist was wrong?
I am stumped, I noticed the pattern in the digits of the numbers, but I do not see how I can link that to the possibility of forming such a statement with those numbers when n is greater than 2.

 Recognitions: Gold Member x==1Mod 5, Y==1 Mod 5, Z==0 Mod 5.