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Abstract
We give a characterization when a nonzero square matrix with integer entries is periodic using cyclotomic polynomials. We also determine the set of all possible periods of periodic matrices with integer entries via Euler Phi functions.
2020 Mathematics Subject Classification:
Acknowledgments
The authors would like to express their thanks to the anonymous referee for his or her valuable comments on the original draft.
Additional information
Funding
The first-named author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (NRF-2019R1F1A1061300). The second-named author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (NRF-2020R1A2C1A01006338).