Abstract
There are many possible proofs of Fermat’s little theorem. Among them we exemplify those using necklaces and dynamical systems. Both methods lead to a generalization. It is a congruence theorem that is already known from Gauss and Gegenbauer. A natural result from these proofs is a bijection between aperiodic necklaces and circle maps.
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Acknowledgements
JB acknowledges partial support from FCT through Financiamento Base 2010-ISFL-1-209. CS acknowledges support from FCT through grant SFRH/77623/2011.
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Serpa, C., Buescu, J. (2014). A Dynamical Approach to Congruences: Linking Circle Maps and Aperiodic Necklaces. In: Grácio, C., Fournier-Prunaret, D., Ueta, T., Nishio, Y. (eds) Nonlinear Maps and their Applications. Springer Proceedings in Mathematics & Statistics, vol 57. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9161-3_15
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DOI: https://doi.org/10.1007/978-1-4614-9161-3_15
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