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Zagier, D. (1990) A one-sentence proof that every prime p ≡ 1 mod 4 is a sum of two squares, American Mathematical Monthly, 97 (2): 144.

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Article

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

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

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


Turkish Journal of Analysis and Number Theory. 2026, Vol. 14 No. 1, 1-5
DOI: 10.12691/tjant-14-1-1
Copyright © 2026 Science and Education Publishing

Cite this paper:
Arto Adili, Adrian Naço, 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.

Correspondence to: Arto  Adili, Department of Mathematics and Physics, “Fan S. Noli” University, Korçë, Albania. Email: aadili@unkorce.edu.al

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.

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