Source: Andrej Cherkaev's List of Puzzles
A computer scientist claims that he proved somehow that the Fermat theorem is correct for the following 3 numbers:
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?
Solution posted by a lot of people in comments!