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Li, H.-L., Fang, S.-C. and Kuo, W. (2026) A Sufficient Condition for the Primality of the Sum of Two Squares. Advances in Pure Mathematics, 16, 412-415.
https://doi.org/10.4236/apm.2026.166022

has been cited by the following article:

• TITLE: Elaborating the Condition in Fermat’s Two Square Theorem

  AUTHORS: Nianrui Lin

  KEYWORDS: Fermat’s Two Square Theorem, Primality, Sum of Two Squares

  JOURNAL NAME: Advances in Pure Mathematics, Vol.16 No.9, September 20, 2026

  ABSTRACT: It is a well-known result that prime numbers congruent to 1 modulo 4 are representable as a sum of two squares. A recent article shows that the number of representations can imply the primality of square-free integers congruent to 1 modulo 4. However, the authors did not clarify the distinctness of the construction of representations in the proof of the main theorem. We provide a complementary proof to clarify this construction and also present an alternative proof based on Jacobi’s two square theorem.