TITLE:
A Sufficient Condition for the Primality of the Sum of Two Squares
AUTHORS:
Han-Lin Li, Shu-Cherng Fang, Way Kuo
KEYWORDS:
Fermat, Brahmagupta-Fibonacci Identity, Primality
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.16 No.6,
June
11,
2026
ABSTRACT: The famous Fermat’s Christmas Theorem states that all Pythagorean primes can be expressed as a sum of two squares of integers. This report specifies the conditions that a (
4k+1
)-type integer expressed in a sum of two squares becomes prime.