A note on Buchi´s problem for p-adic numbers

Marianela Castillo


We prove that for any prime p and any integer k > 2,there exist in the ring Zpof p-adic integers arbitrarily long sequences whose sequence of k-th powers1)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.

Texto completo:



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DOI: http://dx.doi.org/10.4067/S0716-09172011000300002

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