關(guān)于一類丟番圖方程整數(shù)解的討論與研究.pdf

1、留796553分類號(hào)：——密級(jí)：?jiǎn)挝淮a：——10697學(xué)號(hào)：2QQ22282西北大學(xué)碩士學(xué)位論文題目：苤士二差垂查圖壅堡整墼鰱煎盟縫魚盟塞作者：窶嚏蓬指導(dǎo)教師塞壁專業(yè)技術(shù)職務(wù)墼撞學(xué)科(專業(yè))基礎(chǔ)熬生答辯日期2QQ曼亙學(xué)位授予日期二零零五年四月AbstractDiophantineequationisanimportantsubjectinnumbertheoryItwasgreatlyconnectedwithalgebra，comb

2、inatorialmathematicsandcomputerscienceetcTheachievementsindiophantineequationsplayanimportantrolebothineverybranchofmathematicsandinothersubjects，suchasphysics，economicsSotherearestillmanypeoplewhohavegreatinterestedindi

3、ophantineequationsIn1999，thediophantineequation2222Ⅳ2322=16xyzappearedinconnectionwiththedescriptionofthelowerpartoftheapproximationspectrurnforquaternion，whichinspireUStostudysuchkindofdiophantineequationo茁2by2cz2=mdxyz

4、fortheconvenienceoftheapplicationinotherfieldsOnconditionsthata，b，C，dareallpositiveintegersandmisanon—negativeinteger，andⅡfd，bjd，cd，themainresultsofthispaperisfirstlygivingthemethodstosolvetheequationnz2by2CZ2=mdxyz，thec

5、ongruentmethodandthemethodofthePell’sequationNext，Ifind(a，b，C，d，m)，whichmaketheequationax2by2cz2=mdxyzhassomefundamentalsolution(s)，andallthecorrespondingfundamentalsolutionsgivenindifferenttabularsTheneveryintegersoluti

6、ontotheequationcomesthroughtheneighbouringprocessfromauniquefundamentalsolutionFinallytheintegersolutionssarisfyingsomeconditionstothediophantineequationax2by2c名2=。dxyzweregivenAuthor：阢“枷版Directedbyy認(rèn)馳』nKeywords：Diophant