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 |
Keywords
- Polynomial Pell's equations
ASJC Scopus subject areas
- Algebra and Number Theory
Cite this
Nonmonic polynomial Pell's equations. / Yokota, H.
In: JP Journal of Algebra, Number Theory and Applications, Vol. 24, No. 1, 02.2012, p. 89-104.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Nonmonic polynomial Pell's equations
AU - Yokota, H.
PY - 2012/2
Y1 - 2012/2
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
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 -