A Note on Büchi's Problem for p-adic numbers
We prove that for any prime p and any integer k > 2, there exist in the ring Zp of p-adic integers arbitrarily long sequences whose sequence of k-th powers 1) has its k-th difference sequence equal to the constant sequence (k!); and 2) is not a sequence of consecutive k-th powers. This shows that the analogue of Buchi's problem for higher powers has a negative answer over Zp. This result for k = 2 was recently obtained by J. Browkin.
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| Format: | Digital revista |
| Language: | English |
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Universidad Católica del Norte, Departamento de Matemáticas
2011
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| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000300002 |
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