The Diophantine equation x^n + y^n = z^n where x, y, z and n are integers, has no non-zero solutions for n>2 has come to be known as Fermat\'s Last Theorem. It was called a \"theorem\" on the strength of Fermat\'s statement, \"It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain.\"
(Note that the restriction n>2 is obviously necessary since there are a number of elementary formulas for generating an infinite number of Pythagorean triples (x, y, z) satisfying the equation for x^2 + y^2 = z^2.)
Andrew Wiles provided a partial proof in 1993 which was then updated by Wiles and R. Taylor in late 1994. Most mathematicians seem satisfied that the theorem has been proved.
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Did you mean Fermat's last theorem?Fermat's last theorem states that no three positive integers a,b,and c can satisfy the equation an+bn=cn(where 'n' is the power of a,b,c)for any integer value of n>2.The equation is a Diophantine equation named after 3rd century alexandrian mathematicianDiophantus.Fermat provedwith n=4 by the method of infinite descent,which reduced the problem to solveonly for all odd prime exponents.In 18th & 19th centuries,Leonhard Euler,Carl Freidrich Gauss,Adrien-Marie legendre,Peter Dirichletand Gabriel Lame provided proofs for n=3,5,and7.