Nonmonic polynomial Pell's equations

H. Yokota

Research output: Contribution to journalArticle

Abstract

The nonmonic polynomial Pell's equation is X 2 - DY 2 = 1, where X, Y and D = A 2 + 2C must be polynomials over Z. Let π be the smallest product of distinct odd primes satisfying πB = πA/C ∈ Z[x]. Then necessary and sufficient conditions for which the polynomial Pell's equation has nontrivial solutions in Z[x] are obtained.

Original languageEnglish
Pages (from-to)89-104
Number of pages16
JournalJP Journal of Algebra, Number Theory and Applications
Volume24
Issue number1
Publication statusPublished - 2012 Feb 1

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Keywords

  • Polynomial Pell's equations

ASJC Scopus subject areas

  • Algebra and Number Theory

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