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.
|ジャーナル||JP Journal of Algebra, Number Theory and Applications|
|出版物ステータス||Published - 2012 2 1|
ASJC Scopus subject areas
- Algebra and Number Theory