Geometric approach to the proof of Fermat’s last theorem
نویسندگان
چکیده
A geometric approach to the proof of Fermat’s last theorem is proposed. Instead integers a, b, c, considers a triangle with side lengths c. It proved that in case right-angled and obtuse-angled triangles Fermat's equation has no solutions. When considering when c are sides an acute triangle, it entire solutions for p>2. The numbers a=k, b=k+m, c=k+n, where k, m, n natural satisfying inequalities n>m, n<k+m, exhaust all possible variants which triangle.
 this carried out by introducing new auxiliary function f(k,p)=kp+(k+m)p–(k+n)p two variables, polynomial degree variable . study necessary out. special proved, variables take consecutive integer values. was stages. Namely, values n, p were considered, following conditions: firstly, number (np–mp) odd, secondly, even, free member f(k, p).
 Another proposed, relationships between supposed solution p)=0 corresponding considered.
 using mathematical apparatus theory integers, elements higher algebra foundations analysis. These studies continuation author's works, some cases
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ژورنال
عنوان ژورنال: Eureka: Physics and Engineering
سال: 2022
ISSN: ['2461-4254', '2461-4262']
DOI: https://doi.org/10.21303/2461-4262.2022.002488