Number Theory

    

Classification of Pythagorean Triples and Reflection on Fermat’s Last Theorem

Authors: Kuan Peng

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.

Comments: 22 Pages.

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Submission history

[v1] 2025-07-19 22:48:56
[v2] 2025-07-25 21:35:53

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