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<p>In this paper, we study several Diophantine equations, like the one involved in Last Fermat’s Theorem and Beal’s equation, over the rings of polynomials and formal power series with coefficients on characteristic zero unique factorization domains. Moreover, we give general estimates of their number of polynomial solutions. Moreover, we study (non)extensions of Fermat’s little theorem and the (non)existence of Wieferich primes over the univariate formal power series ring with real coefficients.</p>

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On (non)extensions of Fermat’s Last Theorem and Beal’s conjecture over polynomial and formal power series rings

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • Danny A. J. Gómez-Ramírez,
  • Alberto F. Boix

摘要

In this paper, we study several Diophantine equations, like the one involved in Last Fermat’s Theorem and Beal’s equation, over the rings of polynomials and formal power series with coefficients on characteristic zero unique factorization domains. Moreover, we give general estimates of their number of polynomial solutions. Moreover, we study (non)extensions of Fermat’s little theorem and the (non)existence of Wieferich primes over the univariate formal power series ring with real coefficients.