## Abstract

For a fixed prime p, let C_{p} denote the complex p-adic numbers. For polynomials A, B ε C p [x] we consider decompositions A (x) f^{2} (x) + B (x) g^{2} (x) = 1 of entire functions f, g on C p and try to improve an impossibility result due to A. Boutabaa concerning transcendental f, g. We also provide a new proof of a p-adic diophantic statement due to D. N. Clark, which is an important ingredient of Boutabaa’s method.

Original language | English |
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Pages (from-to) | 68-76 |

Number of pages | 9 |

Journal | P-Adic Numbers, Ultrametric Analysis, and Applications |

Volume | 2 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2010 |

Externally published | Yes |

## Keywords

- p-adic analysis
- p-adic differential equations
- p-adic functional equations

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