# Polynomial Pell's equation-II

W. A. Webb, H. Yokota

2 引用 (Scopus)

### 抄録

The polynomial Pell's equation is X2 - DY2 = 1, where D is a polynomial with integer coefficients and the solutions X, Y must be polynomials with integer coefficients. Let D = A2 + 2C be a polynomial in L[x], where deg C<deg A. Then for pB = pA/C ∈ L[x], p a prime, a necessary and sufficient condition for which the polynomial Pell's equation has a nontrivial solution is obtained. Furthermore, all solutions to the polynomial Pell's equation satisfying the above condition are determined.

元の言語 English 128-141 14 Journal of Number Theory 106 1 https://doi.org/10.1016/j.jnt.2003.12.005 Published - 2004 5 Yes

### ASJC Scopus subject areas

• Algebra and Number Theory

### これを引用

Polynomial Pell's equation-II. / Webb, W. A.; Yokota, H.

：: Journal of Number Theory, 巻 106, 番号 1, 05.2004, p. 128-141.

Webb, WA & Yokota, H 2004, 'Polynomial Pell's equation-II', Journal of Number Theory, 巻. 106, 番号 1, pp. 128-141. https://doi.org/10.1016/j.jnt.2003.12.005
Webb, W. A. ; Yokota, H. / Polynomial Pell's equation-II. ：: Journal of Number Theory. 2004 ; 巻 106, 番号 1. pp. 128-141.
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