What is the current status of Fermats Last Theorem?
In the margin of his copy of a book by Diophantus, Pierre de Fermat wrote that it is possible to have a square be the sum of two squares, but that a cube can not be the sum of two cubes, nor a fourth power be a sum of two fourth powers, and so on. Further, he wrote that he had found a truly marvelous proof which the margin was too small to contain. Fermat’s Last Theorem states that xn + yn = zn has no non-zero integer solutions for x, y and z when n > 2. That is to say, there are no integers x, y, z such that x3 + y3 = z3, or integers x, y, z such that x7 + y7 = z7. Although this is easily stated, it has proved to be one of the most puzzling problems in the whole history of mathematics. Long after all the other statements made by Fermat had been either proved or disproved, this remained; hence it is called Fermat’s Last Theorem (actually, Conjecture would be more accurate than Theorem). This conjecture was worked on by many famous mathematicians. Fermat himself proved this theorem for
