Fermat's last theorem is a mathematical conjecture proposed by Pierre de Fermat in 1637. It 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 2.
Yes, Fermat's last theorem has been proven by Andrew Wiles in 1994 after over 350 years of attempts by mathematicians. Wiles used advanced mathematical techniques, including modular forms and elliptic curves, to prove the theorem.
Fermat's last theorem is significant because it is one of the most famous and long-standing problems in mathematics. It has also inspired the development of new mathematical fields and techniques, such as algebraic number theory and elliptic curves.
Pierre de Fermat was a French mathematician, lawyer, and government official in the 17th century. He is best known for his contributions to number theory, including Fermat's last theorem, and his work in analytic geometry.
Yes, there are several variations and generalizations of Fermat's last theorem, such as the Beal conjecture, which asks for solutions to an + bn = cn where a, b, and c are positive integers and n is a real number greater than 2. There are also generalizations to other number systems, such as complex numbers and Gaussian integers.