**Jack Dikian**

**November 2011**

The theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two.

**Fermat**'s last theorem has been one of the most difficult problems to solve. It took over 350 years to solve and has precipitated more incorrect proofs than any other math problem.
In 1995

**Andrew Wiles**released his 108-page proof after spending almost 7 years developing it. The proof is regarded to be one of the most complicated in mathematics and involved (chapters in Wiles’ paper) Galois representations, cohomology groups, Gorenstein property, congruences between Hecke rings, Selmer group, elliptic curves, Gorenstein rings and local complete intersections.**The Simpsons**. In the episode “Treehouse of Horror VI” a sum, proved impossible by the theorem, the equation 1782

^{12}+ 1841

^{12}= 1922

^{12}is visible. The joke being that the twelfth root of the sum does evaluate to 1922 due to rounding errors. Note that the left hand side is odd, while 1922

^{12}is even, so the equality cannot hold. Instead of 1922, it actually is 1921.999999995.