Pierre de Fermat Fermat’s Last Theorem is one of the most famous and intriguing problems in the history of mathematics. It states as follows, Theorem (Fermat's Last Theorem ) No three positive integers x,y, and z can satisfy the equation xn+yn=zn for any integer n greater than 2. For example, there are no positive integers x, y, and z such that x3+y3=z3 (the sum of two cubes is not a cube). This simple-looking equation has fascinated mathematicians for centuries. It was first stated by Pierre de Fermat, a French lawyer and amateur mathematician, around 1637 in the margin of a copy of Arithmetica by Diophantus of Alexandria, an ancient Greek algebra book. Fermat wrote: “It is impossible for a cube to be a sum of two cubes, a fourth power to be a 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 remarkable proof [of this theorem], but this margin is too...