@article{tjant20261413,
author={{Adili, Arto and Na?o, Adrian and Kelo, Lorena},
title={An Elementary Method for Determining the Quadratic Character of -1, 2, 3 and 5 Modulo Primes},
journal={Turkish Journal of Analysis and Number Theory},
volume={14},
number={1},
pages={23--28},
year={2026},
url={https://pubs.sciepub.com/tjant/14/1/3},
issn={2333-1232},
abstract={We provide elementary proofs of the classical quadratic-residue criteria for -1, 2, 3, and 5 modulo odd primes. In addition, we determine the quadratic character of the integers <i>a</i> and <i>b</i> in the prime representations <i>p=a</i><SUP><i>2</i></SUP><i>+b</i><SUP><i>2</i></SUP><i> </i>and <i>p=a</i><SUP><i>2</i></SUP><i>+2b</i><SUP><i>2</i></SUP>. These results further illustrate the relationship between quadratic residues and binary quadratic forms.},
doi={10.12691/tjant-14-1-3}
publisher={Science and Education Publishing}
}