抄録
Let D=F2+2G be a monic quartic polynomial in Z[x], where degG<degF. Then for F/G∈Q[x], a necessary and sufficient condition for the solution of the polynomial Pell's equation X2-DY2=1 in Z[x] has been shown. Also, the polynomial Pell's equation X2-DY2=1 has nontrivial solutions X,Y∈Q[x] if and only if the values of period of the continued fraction of D are 2, 4, 6, 8, 10, 14, 18, and 22 has been shown. In this paper, for the period of the continued fraction of D is 4, we show that the polynomial Pell's equation has no nontrivial solutions X,Y∈Z[x].
本文言語 | English |
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ページ(範囲) | 2003-2010 |
ページ数 | 8 |
ジャーナル | Journal of Number Theory |
巻 | 130 |
号 | 9 |
DOI | |
出版ステータス | Published - 2010 9月 |
外部発表 | はい |
ASJC Scopus subject areas
- 代数と数論