Abstract
Löschian numbers are a topic of investigation in scientific fields such as spatial economics, socio-economic geography, geometry, and number theory. This is because these numbers play a significant role in the optimization of spatial interactions, in terms of achieving the best division of space between competing central places. This work presents four new number theoretic theorems and four corollaries concerning the properties of Löschian numbers, which enable a better understanding of the mathematical properties of these numbers.
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