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A Sufficient Condition for the Primality of the Sum of Two Squares
Department of Computer Science, City University of Hong Kong, Hong Kong SAR, China
Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, USA
Hong Kong Institute for Advanced Study, City University of Hong Kong, Hong Kong SAR, China
- 1 Department of Computer Science, City University of Hong Kong, Hong Kong SAR, China
- 2 Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, USA
- 3 Hong Kong Institute for Advanced Study, City University of Hong Kong, Hong Kong SAR, China
Advances in Pure Mathematics·Volume 16 (2026)·Pages 412–415·Published 5 June 2026·DOI10.4236/apm.2026.166022
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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 ( 4 k + 1 )-type integer expressed in a sum of two squares becomes prime.
KeywordsFermatBrahmagupta-Fibonacci IdentityPrimality
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