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Student Number 88221010
Author Zhen-Yu Gu(顧震宇)
Author's Email Address No Public.
Statistics This thesis had been viewed 1961 times. Download 848 times.
Department Mathematics
Year 2000
Semester 2
Degree Master
Type of Document Master's Thesis
Language zh-TW.Big5 Chinese
Title 關於方程式 x^2+11=p^n 的研究
Date of Defense 2001-07-04
Page Count 25
Keyword
  • Nagell
  • Ramanujan
  • Abstract none
    Table of Content 1.緣由...................1
    2.定義及相關定理.........3
    3.方程式x^2+11=p^n.......8
    3.1 方程式 x^2+11=3^n...8
    3.2 方程式 x^2+11=p^n...17
    Reference ibitem{Alt} R. Alter and K.K. Kubota, {it The Diophantine equation $x^2+11=3^n$ and a related sequence}, J. Number Theory 7
    (1975), 5-10.
    ibitem{Ben} E. Bender and N. Herzberg, {it Some Diophantine equation related to quadratic form $ax^2+by^2$}, in " Studies
    in Algebra and Number Theory," Advances in Mathematics Supplementary Studies, Vol. 6, pp. 219-272, Academic Press, New York,
    1979.
    ibitem{Sho} Y. Bugeaud and T.N. Shorey , {it On The Number of Solutions of The Generalized Ramanujan-Nagell Equation}. J.
    Reine Angew. Math., to appear.
    ibitem{Coh1} E.L. Cohen, {it Sur certaines $acute{e}$quations diophantiennes quadratiques}, C. R. Acad. Sci. Paris S$acute{e}$r. A 274 (1972), 139-140.
    ibitem{Coh2} E.L. Cohen, {it Sur $l^{'}acute{e}$quation diophantienne $x^2+11=3^k$}, C.R. Acad. Sci. Paris S$acute{e}$r. A 275 (1972), 5-7.
    ibitem{Coh3} E.L. Cohen, {it On dionphantine equations of the form $x^2+D=p^k$}, Enseignement Math. (2), 20 (1974), 235-241.
    ibitem{Coh} E.L. Cohen, {it The Diophantine Equation $x^2+11=3^k$ and Related Questions}, Math.
    Scand., 38 (1976), no.2, 240-246.
    ibitem{Hun} T.W. Hungerford, {it Algebra}, Fourth printing, Springer-Verlag, 1987.
    ibitem{Joh} W. Johnson, {it The Diophantine Equation $x^2+7=2^n$}, Amer. Math. Monthly, 94 (1987), no.1, 59-62.
    ibitem{Mar} D.A. Marcus, {it Number fields}, Second printing, Springer-Verlag, 1987.
    ibitem{Mor} L.J. Mordell, {it Diophatine equation (Pure and Applied Math. 30)}, Academic Press, New York, 1969.
    ibitem{Nag} T. Nagell, {it The Diophatine Equation $x^2+7=2^n$}, Ark. Mat., 4 (1961), 185-187.
    ibitem{Niv} I. Niven, H.S. Zuckerman, H.L. Montgomery, {it An Introduction to the Theory of Numbers}, 5th ed., John Wiley
    and Sons, 1991.
    ibitem{Sko} Th. Skolem, S. Chowla and D.J. Lewis, {it The Diophantine equation $2^{n+2}-7=x^2$ and related problems}, Proc. Amer. Math. Soc. 10 (1959)
    , 663-669.
    ibitem{Ca} 康明昌, {it 近世代數}, 1st ed., 聯經出版事業公司, 1988 .
    Advisor
  • Ming-Guang Leu(呂明光)
  • Files
  • 88221010.pdf
  • approve immediately
    Date of Submission 2001-07-04

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