A New Approach to the Girard-Fermat’s Two Squares Theorem with Some Remarks on Primes’ Decomposition as Sums of Squares

eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2026-03-23 14 1 1 5 10.12691/tjant-14-1-1 TJANT20261411 article A New Approach to the Girard-Fermat’s Two Squares Theorem with Some Remarks on Primes’ Decomposition as Sums of Squares Arto Adili aadili@unkorce.edu.al 1 Adrian Na?o 2 Lorena Kelo 2 Department of Mathematics and Physics, “Fan S. Noli” University, Kor??, Albania Department of Mathematics Engineering, Polytechnic University, Tirana, Albania A new elementary approach to the Girard-Fermat theorem, generalizing the equality of the sum of squares with the prime to its divisibility by that prime. That reveals some interesting properties of the corresponding decomposition’s components. https://pubs.sciepub.com/tjant/14/1/1/tjant-14-1-1.pdf Girard-Fermat theorem primitive root indexes