phantus' major work is the Arithmetica, of which only a portion has survived.[8] Fermat's conjecture of his Last Theorem was inspired while reading a new edition of the Arithmetica,[9] which was translated into Latin and published in 1621 by Claude Bachet.[10]
Diophantine equations have been studied for thousands of years. For example, the solutions to the quadratic Diophantine equation x2 + y2 = z2 are given by the Pythagorean triples, originally solved by the Babylonians (c. 1800 BC).[11] Solutions to linear Diophantine equations, such as 26x + 65y = 13, may be found using the Euclidean algorithm (c. 5th century BC).[12] Many Diophantine equations have a form similar to the equation of Fermat's Last Theorem from the point of view of algebra, in that they have no cross terms mixing two letters, without sharing its particular properties. For example, it is known that there are inf
In number theory, Fermat's Last 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.
This theorem was first conjectured by Pierre de Fermat in 1637, famously in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin. No successful proof was published until 1995 despite the efforts of countless mathematicians during the 358 intervening years. The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th. It is among the most famous theorems in the history of mathematics and prior to its 1995 proof was in the Guinness Book of World Records for "most difficult math problems".
Contents
1 Fermat's conjecture (History)
2 Mathematical context
2.1 Pythagorean triples
2.2 Diophantine equations
3 Fermat's conjecture
4 Proofs for sp www.111com.net ecific exponents
5 Sophie Germain
6 Ernst Kummer and the theory of ideals
7 Mordell conjecture 8 Rational exponents
9 Computational studies
