### 博碩士論文 88221010 詳細資訊

 以作者查詢圖書館館藏 、以作者查詢臺灣博碩士 、以作者查詢全國書目 、勘誤回報 、線上人數：8 、訪客IP：3.234.244.18

 ★ 關於胡-黃-王猜測的研究 ★ 關於 (2,n) 群試問題的研究 ★ 關於方程式2x^2+1=3^n的研究 ★ On problems of certain arithmetic functions ★ 伽羅瓦理論 ★ k階歐幾里得環 ★ On a Paper of P. M. Cohn ★ On some problem in Arithmetic Dynamical System and Diophantine Approximation in Positive Characteristic ★ On Generalized Euclidean Rings ★ ZCm 的理想環生成元個數之上限

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Johnson 的方法來再一次証明由 Cohen 所証明過

x^2+11=p^n

★ Nagell

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

(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 .