一類Pell方程的兩個相關問題.pdf

1、西北大學碩士學位論文一類Pell方程的兩個相關問題姓名：韓小偉申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：袁進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