Panraksa C.Samart D.Sriwongsa S.Mahidol University2023-07-172023-07-172023-01-01Bulletin of the Australian Mathematical Society (2023)00049727https://repository.li.mahidol.ac.th/handle/20.500.14594/87898Niven's theorem asserts that {equation presented}. In this paper, we use elementary techniques and results from arithmetic dynamics to obtain an algorithm for classifying all values in the set {equation presented} where K is an arbitrary number field.MathematicsArticleSCOPUS10.1017/S00049727230004482-s2.0-8516363975717551633