Fermat’s Last Theorem

Fermat’s Last Theorem, in mathematics, famous theorem which has led to important discoveries in algebra and analysis. It was proposed by the French mathematician Pierre de Fermat. While studying the work of the ancient Greek mathematician Diophantus, Fermat became interested in the chapter on Pythagorean numbers—that is, the sets of three numbers, a, b, and c, such as 3, 4, and 5, for which the equation a^2 + b^2 = c^2 is true. He wrote in pencil in the margin, “I have discovered a truly remarkable proof which this margin is too small to contain.” Fermat added that when the Pythagorean Theorem is altered to read a^n + b^n = c^n, the new equation cannot be solved in integers for any value of n greater than 2. That is, no set of positive integers a, b, and c can be found to satisfy, for example, the equation a^3 + b^3 = c^3 or a^4 + b^4 = c^4.
Fermat’s simple theorem turned out to be surprisingly difficult to prove. For more than 350 years, many mathematicians tried to prove Fermat’s statement or to disprove it by finding an exception. In June 1993, Andrew Wiles, an English mathematician at Princeton University, claimed to have proved the theorem; however, in December of that year reviewers found a gap in his proof. On October 6, 1994, Wiles sent a revised proof to three colleagues. On October 25, 1994, after his colleagues judged it complete, Wiles published his proof.
Despite the special and somewhat impractical nature of Fermat’s theorem, it was important because attempts at solving the problem led to many important discoveries in both algebra and analysis.

Note a^n means "a" raised to nth power