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 |
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Keywords
- Polynomial Pell's equations
ASJC Scopus subject areas
- Algebra and Number Theory
Cite this
Yokota, H. (2012). Nonmonic polynomial Pell's equations. JP Journal of Algebra, Number Theory and Applications, 24(1), 89-104.