Author(s)

Balasubramani Prema Rangasamy

Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India.

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 xⁿ + yⁿ = zⁿ 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.

Fermat’s Last Theorem, Fermat’s Conjecture, Euler’s Disproved Conjecture, Other Way of Taxi Cab Number and N-Tangled Object, Root of Prime Bases and Root of Integer Bases

Rangasamy, B. (2020) One More Assertion to Fermat’s Last Theorem. Advances in Pure Mathematics, 10, 359-369. doi: 10.4236/apm.2020.106022.