Powerful arithmetic progressions |
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| Authors: | L. Hajdu |
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| Affiliation: | aUniversity of Debrecen, Institute of Mathematics and the Number Theory Research Group of the Hungarian Academy of Sciences, Debrecen, P.O. Box 12, H-4010, Hungary |
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| Abstract: | We give a complete characterization of so-called powerful arithmetic progressions, i.e. of progressions whose kth term is a kth power for all k. We also prove that the length of any primitive arithmetic progression of powers can be bounded both by any term of the progression different from 0 and ±1, and by its common difference. In particular, such a progression can have only finite length. |
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| Keywords: | Key words and phrases: Perfect powers Arithmetic progression |
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