One More Assertion to Fermat’s Last Theorem

Abstract

Around 1637, Fermat wrote his Last Theorem in the margin of his copy “ It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers ”. With n, x, y, z ∈ N (meaning that n, x, y, z are all positive numbers) and n > 2, the equation x n + y n = z n has no solutions. In this paper, I try to prove Fermat’s statement by reverse order, which means no two cubes forms cube, no two fourth power forms a fourth power, or in general no two like powers forms a single like power greater than the two. I used roots, powers and radicals to assert Fermat’s last theorem. Also I tried to generalize Fermat’s conjecture for negative integers, with the help of radical equivalents of Pythagorean triplets and Euler’s disproven conjecture.