One More Assertion to Fermat’s Last Theorem  

作　　者：Balasubramani Prema Rangasamy Balasubramani Prema Rangasamy(Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India)

机构地区：[1]Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India

出　　处：《Advances in Pure Mathematics》2020年第6期359-369,共11页理论数学进展（英文）

摘　　要：Around 1637, Fermat wrote his Last Theorem in the margin of his copy “<em>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</em>”. With <em>n, x, y, z</em> <span style="white-space:nowrap;">&#8712;</span> <strong>N</strong> (meaning that <em>n, x, y, z</em> are all positive numbers) and <em>n</em> > 2, the equation <em>xⁿ</em> + <em>yⁿ</em> = <em>zⁿ</em>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.Around 1637, Fermat wrote his Last Theorem in the margin of his copy “<em>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</em>”. With <em>n, x, y, z</em> <span style="white-space:nowrap;">&#8712;</span> <strong>N</strong> (meaning that <em>n, x, y, z</em> are all positive numbers) and <em>n</em> > 2, the equation <em>xⁿ</em> + <em>yⁿ</em> = <em>zⁿ</em>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.

关 键 词：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 

分 类 号：O17[理学—数学]