Fermat’s last theorem states that the equation xn + yn = zn has no solutions in integers x, y, z, and n where n > 2. Try this in a calculator: 178212 + 184112 = 192212.
That equation was generated by a program written by David X Cohen, at the time a writer for The Simpsons, subsequently executive producer of Futurama. He put it in the background of the three-dimensional realm in the episode Homer3. It’s not a counter-example to the theorem—which at the time hadn’t been completely proved, but had been proved up to a certain exponent (much higher than 12)—but it will look like one on any calculator that truncates numbers after ten or fewer digits.
Found in a mathematical interview with Cohen.