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

• Castillo, Marianela ^[1]
  1. [1] Universidad de Concepción

     Universidad de Concepción

     Comuna de Concepción, Chile

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 30, Nº. 3, 2011, págs. 295-302
• Idioma: inglés
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• Resumen

  • 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 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.