Fermat's Theorem: A Math Problem and the Smart Boy Who Proved It Wrong

[uranium_235]

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.

 

[robert Ihnot]

x==1Mod 5, Y==1 Mod 5, Z==0 Mod 5.