Criterion for Unique Factorization in Quadratic Orders

Ahmad Issa

International Journal of Mathematics and Mathematical Sciences, 2026, vol. 2026, 1-5

Abstract: This paper addresses the problem of unique factorization in quadratic orders within real quadratic fields. We establish a necessary and sufficient condition for a quadratic order OΔ, where Δ is a positive fundamental discriminant, to be a unique factorization domain (UFD). Our criterion is based on the solvability of certain Diophantine equations of the form x2−dy2=c2p, where p is a prime number satisfying specific conditions related to Δ.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:8816494

DOI: 10.1155/ijmm/8816494

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