Kuan Peng, July 2025 « Classification of Pythagorean triples and reflection on Fermat’s last theorem»
Pythagorean triples are generated with Euclid’s formula. But how this formula was derived by or before Euclid is a mystery. We have derived Euclid’s formula directly from Pythagorean equation and classified all Pythagorean triples in a 3D table. The equation
X^2+Y^j=Z^2 is proven to have infinitely many integer solutions. By comparing Pythagorean equation with Fermat’s equation for n=3 we were able to explain why Fermat’s equation with n=2 has integer solutions while with n > 3 it has not. We propose an algebraic method to work Fermat’s last theorem.
https://pengkuanonmaths.blogspot.com/2025/07/classification-of-pythagorean-triples.html