One More Assertion to Fermat’s Last Theorem

• 作者: Balasubramani Prema Rangasamy
• 来源期刊: 理论数学进展(英文)
• 学科: 数学
• 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
• 年，卷（期）: llsxjzyw_2020,（6）
• 页码范围: 359-369
• 页数: 11页
• 分类号: O17

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.