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

Arto Adili^1, , Adrian Naço² and Lorena Kelo¹

¹Department of Mathematics and Physics, “Fan S. Noli” University, Korçë, Albania

²Department of Mathematics Engineering, Polytechnic University, Tirana, Albania

Cite this paper:
Arto Adili, Adrian Naço and Lorena Kelo. A New Approach to the Girard-Fermat’s Two Squares Theorem with Some Remarks on Primes’ Decomposition as Sums of Squares. Turkish Journal of Analysis and Number Theory. 2026; 14(1):1-5. doi: 10.12691/tjant-14-1-1

Abstract

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.

Keywords:
Girard-Fermat theorem primitive root indexes

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