FERMAT LAST THEOREM : NUMBER THEORY

                         FERMAT'S LAST THEOREM 

HISTORY: Pierre de Fermat was a French lawyer at the Parliament of Toulouse, France. He was born in between 31 October and 6 december, 1607 and passed away in 12 january, 1665. His intelligence was not only bounded into the court room, he was also a successful mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. He had a great interest in number theory, and his research made number theory more easy. he also has a lot of contributions to Analytic geometry, Probability and optics. he is very famous for his Fermat's principle for light propagation and his Fermat's Last Theorem, which he described in a note at the margin of a copy of Diophantus' Arithmetica. 

Short Description about him :

Born	Between 31 october - 6 December 1607
Place of Birth	Beaumont-de-Lomagne, France
Education	College de Navarre, University of Orleans (L.L.B. , 1626)
Famous for	Fermat's principle for light propagation, Fermat's Last Theorem etc.
Fields	Law and Mathematics
Died	12 January, 1665 , in Castres, France

 THEOREM :

In number theory Fermat's Last Theorem (also known as Fermat's conjecture) states that no three positive integers  a, b, and c satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known to have infinitely many solutions since antiquity.

Note that the restriction  is obviously necessary since there are a number of elementary formulas for generating an infinite number of Pythagorean triples  satisfying the equation for ,

Diophantus' Arithmetica, 1670 edition

This theorem was first guessed by Pierre de Fermat in 1637 in the margin of a copy of Diophantus' Arithmetica. The first successful proof of this equation was first proposed by Andrew Wiles in 1994, after 358 years of the creation of the theorem. This theorem also proved much of the Modularity Theorem. Modularity theorem was proved in 20th century. It was in the Guinness Book of World Records as the "most difficult mathematical problem".