An extension of Büchi's problem for polynomial rings in zero characteristic

Author:
Hector Pasten

Journal:
Proc. Amer. Math. Soc. **138** (2010), 1549-1557

MSC (2010):
Primary 11U05, 12L05; Secondary 11C08

DOI:
https://doi.org/10.1090/S0002-9939-09-10259-9

Published electronically:
December 29, 2009

MathSciNet review:
2587438

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove a strong form of the `` Squares Problem'' over polynomial rings with characteristic zero constant field. In particular we prove : for all there exists an integer depending only on such that, if are distinct elements of and we have polynomials , with some non-constant, satisfiying the equations for each , then is the zero polynomial.

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Additional Information

**Hector Pasten**

Affiliation:
Departamento de Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Concepción, Chile

Email:
hpasten@gmail.com

DOI:
https://doi.org/10.1090/S0002-9939-09-10259-9

Keywords:
B\"uchi's problem,
squares problem,
polynomials,
Hilbert's tenth problem

Received by editor(s):
September 2, 2008

Received by editor(s) in revised form:
March 12, 2009

Published electronically:
December 29, 2009

Communicated by:
Julia Knight

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.