Nonmonic polynomial Pell's equations

H. Yokota

Nonmonic polynomial Pell's equations

H. Yokota

Systems Engineering and Science

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	89-104
Number of pages	16
Journal	JP Journal of Algebra, Number Theory and Applications
Volume	24
Issue number	1
Publication status	Published - 2012 Feb 1

Keywords

Polynomial Pell's equations

ASJC Scopus subject areas

Algebra and Number Theory

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