Abstract
In this paper, we prove the existence of three pairwise distinct families of totally real bi-quadratic fields, each having Pólya group isomorphic to Z/2Z. This extends the previously known families of number fields considered by Heidaryan and Rajaei. Our results also establish that under mild assumptions, the possibly infinite families of bi-quadratic fields having a non-principal Euclidean ideal class, considered by Chattopadhyay and Muthukrishnan, fail to be Pólya fields.
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