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

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A computer scientist claimed to have proven Fermat's Last Theorem for three specific numbers but was challenged by a 10-year-old boy who identified a mistake. The boy pointed out that the theorem cannot hold for those numbers, prompting the scientist to check his calculations and discover a bug in his computer program. The discussion highlights the importance of understanding modular arithmetic, as the boy noted the numbers' patterns in relation to modulo 5. The conversation revolves around the implications of these findings and the mathematical principles involved. Ultimately, the incident underscores the significance of critical thinking in mathematics.
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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.
 
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x==1Mod 5, Y==1 Mod 5, Z==0 Mod 5.
 

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