ELEMENTARY PROOFS FOR THE FERMAT'S LAST THEOREM IN Z USING ONE TRICK FOR A RESTRICTION IN ZP

被引：1

作者：

Klykov, Sergey P. ^{[1
]}

机构：

[1] Alpha Integrum Ltd, Serpukhov District 142279, Moscow Region, Russia

来源：

JOURNAL OF SCIENCE AND ARTS | 2023年 / 03期

关键词：

Fermat's last theorem; Pythagorean theorem; p-adic integers; numbers; integers;

D O I：

10.46939/J.Sci.Arts-23.3-a03

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

An elementary and short proof of Fermat's Last Theorem (FLT) is presented, which is understandable even to a student. Perhaps this proof is precisely the lost proof, which could similar to own Fermat's proof. Restricting some coefficients of polynomials by value 0, except for the first term, allows to prove the Fermat's Last Theorem for domain Z, since in this case the canonical representation of p-adic numbers is limited to only one digit in the corresponding p-ary system. It was shown within the framework of elementary algebra, which corresponds to the Pythagorean theorem (PT) that the assumption of the existence of certain "Fermat's triples" (FT), as integer solutions of Fermat's Last Theorem, can not be possible in Z due to some fatal inconsistencies for the PT and found by means the PT. Some equations in Z(p) were shown for n=3, 4 and 5.

引用

页码：603 / 608

页数：6