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...
Guardado en:
| Autor principal: | |
|---|---|
| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2011
|
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000300002 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| id |
oai:scielo:S0716-09172011000300002 |
|---|---|
| record_format |
dspace |
| spelling |
oai:scielo:S0716-091720110003000022012-06-18A Note on Büchi's Problem for p-adic numbersCastillo,MarianelaWe 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.30 n.3 20112011-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000300002en10.4067/S0716-09172011000300002 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| description |
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. |
| author |
Castillo,Marianela |
| spellingShingle |
Castillo,Marianela A Note on Büchi's Problem for p-adic numbers |
| author_facet |
Castillo,Marianela |
| author_sort |
Castillo,Marianela |
| title |
A Note on Büchi's Problem for p-adic numbers |
| title_short |
A Note on Büchi's Problem for p-adic numbers |
| title_full |
A Note on Büchi's Problem for p-adic numbers |
| title_fullStr |
A Note on Büchi's Problem for p-adic numbers |
| title_full_unstemmed |
A Note on Büchi's Problem for p-adic numbers |
| title_sort |
note on büchi's problem for p-adic numbers |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2011 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000300002 |
| work_keys_str_mv |
AT castillomarianela anoteonbuchisproblemforpadicnumbers AT castillomarianela noteonbuchisproblemforpadicnumbers |
| _version_ |
1718439778173583360 |