Abstract
We investigate polynomial values of sums of products of consecutive integers. For the degree two case we give effective finiteness results, while for the higher degree case we provide ineffective finiteness theorems. For the latter purpose, we also show that the polynomials corresponding to the sums of products we investigate, are indecomposable.
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Acknowledgements
The work is supported by the EFOP-3.6.1-16-2016-00022 and EFOP-3.6.2-16-2017-00015 projects. The projects are co-financed by the European Union and the European Social Fund. The research of the first three authors was supported in part by the Hungarian Academy of Sciences and by the NKFIH Grants NK104208 and K115479. The second author was supported by the János Bolyai Scholarship of the Hungarian Academy of Sciences. Research of F. L. was supported in part by Grants CPRR160325161141 and an A-rated researcher award both from the NRF of South Africa and by Grant No. 17-02804S of the Czech Granting Agency. Furthermore, this work started during a visit of F. L. at the Mathematical Institute of the University of Debrecen in July 2016. This author thanks that institution for its hospitality and support.
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Communicated by A. Constantin.
Dedicated to Professor Ákos Pintér on the occasion of his 50th birthday.
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Bazsó, A., Bérczes, A., Hajdu, L. et al. Polynomial values of sums of products of consecutive integers. Monatsh Math 187, 21–34 (2018). https://doi.org/10.1007/s00605-017-1130-2
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DOI: https://doi.org/10.1007/s00605-017-1130-2