Abstract
Let pa be a prime power and n0 a square-free number. We prove that any complementing pair in a cyclic group of order pan0 is quasi-periodic, with one component decomposable by the the subgroup of order p. The proof is by induction and reduction since the presence of the square-free factor n0 allows us to perform a Tijdeman decomposition. We also give an explicit example to show that \(\mathbb{Z}_{72}\) is the smallest cyclic group that fails to have the strong Tijdeman property.
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Zhou, W. Quasi-periodicity of \(\mathbb {Z}_{p^an_0}\). Acta Math. Hungar. 170, 645–654 (2023). https://doi.org/10.1007/s10474-023-01361-3
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DOI: https://doi.org/10.1007/s10474-023-01361-3