1、西北大學(xué)碩士學(xué)位論文一類Pell方程的兩個(gè)相關(guān)問題姓名：韓小偉申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：袁進(jìn)20090610TworelatedissuesforaclassofPell’SequationAbstractPell’sequationisoneoftheoldestproblemsstudiedinnumbertheoryastheclassicrepresentationofthequadraticDiophantin

2、eequation，Pell’Sequationhasalwaysbeenconcemedbyscholarsspecializedinnumbertheoryparticularlyrelatingtoresearch戈2一By2=1，andmanyhavemadeconsiderableachievements，someoftheseresultsforsolvingtheexistenceofsolutionsofsomeDiop

3、hantineequationsareveryhelpfulHoweversolvingX2一By2=1amountstosolvingtheminimumsolution，butitisverydifficultWhetherbytrialorevenscoresoflawareoftenencounteredinthelongcalculation，andonlytosolvespecificvaluesofDTherefore，l

4、ookingforthesimplemethodsforsolvingtheminimumsolutionandexploringtheapplicationvalueofthePell’sequationareimportantsubjectsinnumbertheoryThemainachievementscontainedinthisdissertationareasfollows：1Usingtheelementarymetho

5、dtodiscussedtherelationshipoftheminimumsolutionsbetweenthePell’Sequation石2一印2=1andx2D1Y2=I(D=d2D1)whered=23，52UsingsomeresultsofthePell’Sequations，theexistenceofsolutionsoftwoclassesofcubicDiophantineequationsisdiscussed