TITLE:
One More Assertion to Fermat’s Last Theorem
AUTHORS:
Balasubramani Prema Rangasamy
KEYWORDS:
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
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.10 No.6,
June
30,
2020
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 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.