On Quadratic Units with a Given Model and Related to Some Diophantine Equations(英文)

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概要

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• Let a_1, a_2,…, a_n with positive rational integers be a sequence which satisifies a_1=a_n, a_2=a_<n-1>,… and let [a_1, a_2,…, a_n]+ω be the continued fraction. Put [numerical formula]. We ask whether there exist ω=√<y>+[y] such that ε=Pω+Q is a quadratic unit, where the symbol [・] denotes the Gauss symbol. As an another problem, we will show that a equation y=a^2+2^m=b^2+2^n with positive rational integers a, b, m, n (m>n, a≡b≡1 (mod 2)) give the minimal quadratic unit [numerical formula] for suitable conditions, where d=(m-2, n-2).

• 八代工業高等専門学校の論文
• 2006-03-01

著者

• 元田 康夫

  Faculty of General Education

関連論文

• On the Constructive Number of a Number and its Application
• On Quadratic Units with a Given Model and Related to Some Diophantine Equations(英文)

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