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

Fingerprint Dive into the research topics of 'Nonmonic polynomial Pell's equations'. Together they form a unique fingerprint.

Cite this

@article{918237bf66c64d1280f6a957ed41c5f6,

title = "Nonmonic polynomial Pell's equations",

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.",

keywords = "Polynomial Pell's equations",

author = "H. Yokota",

year = "2012",

month = feb,

day = "1",

language = "English",

volume = "24",

pages = "89--104",

journal = "JP Journal of Algebra, Number Theory and Applications",

issn = "0972-5555",

publisher = "Pushpa Publishing House",

number = "1",

}

TY - JOUR

T1 - Nonmonic polynomial Pell's equations

AU - Yokota, H.

PY - 2012/2/1

Y1 - 2012/2/1

N2 - 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.

AB - 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.

KW - Polynomial Pell's equations

UR - http://www.scopus.com/inward/record.url?scp=84858955628&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858955628&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84858955628

VL - 24

SP - 89

EP - 104

JO - JP Journal of Algebra, Number Theory and Applications

JF - JP Journal of Algebra, Number Theory and Applications

SN - 0972-5555

IS - 1

ER -

Nonmonic polynomial Pell's equations

Abstract

Keywords

ASJC Scopus subject areas

Other files and links

Cite this