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Polynomial Pell's equation–II

✍ Scribed by W.A. Webb; H. Yokota

Book ID
104024400
Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
248 KB
Volume
106
Category
Article
ISSN
0022-314X

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✦ Synopsis

The polynomial Pell's equation is X 2 À DY 2 ¼ 1; where D is a polynomial with integer coefficients and the solutions X ; Y must be polynomials with integer coefficients. Let D ¼ A 2 þ 2C be a polynomial in Z½x; where deg Codeg A: Then for pB ¼ pA=CAZ½x; 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.

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