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1、INSTRUCTOR’SSOLUTIONSMANUALtoaccompanyELEMENTARYNUMBERTHEORYANDITSAPPLICATIONSFIFTHEDITIONBartGoddardKennethH.RosenAT&TLabsThisworkisprotectedbyUnitedStatescopyrightlawsandisprovidedsolelyfortheuseofinstructorsinteachingtheircoursesandassessingstudentlearning.Dis
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3、ctedtoabidebytheserestrictionsandtohonortheintendedpedagogicalpurposesandtheneedsofotherinstructorswhorelyonthesematerials.ReproducedbyPearsonAddison-Wesleyfromelectronicfilessuppliedbytheauthor.Copyright?2005PearsonEducation,Inc.PublishingasPearsonAddison-Wesley
4、,75ArlingtonStreet,Boston,MA02116.Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recording,orotherwise,withoutthepriorwrittenpermissionofthepublisher.Printed
5、intheUnitedStatesofAmerica.ISBN0-321-26842-3123456XXX0807060504CHAPTER1TheIntegers1.1.Numbers,Sequences,andSums1.1.1.a.Thesetofintegersgreaterthan3iswell-ordered.Everysubsetofthissetisalsoasubsetofthesetofpositiveintegers,andhencemusthavealeastelement.b.Thesetofe
6、venpositiveintegersiswell-ordered.Everysubsetofthissetisalsoasubsetofthesetofpositiveintegers,andhencemusthavealeastelement.c.Thesetofpositiverationalnumbersisnotwell-ordered.Thissetdoesnothavealeastelement.Ifa=bweretheleastpositiverationalnumberthena=(b+a)wouldb
7、easmallerpositiverationalnumber,whichisacontradiction.d.Thesetofpositiverationalnumbersoftheforma=2iswell-ordered.Considerasubsetofnumbersofthisform.Thesetofnumeratorsofthenumbersinthissubsetisasubsetofthesetofpositiveintegers,soitmusthavealeastelementb.Thenb=2is
8、theleastelementofthesubset.e.Thesetofnonnegativerationalnumbersisnotwell-ordered.Thesetofpositiverationalnumbersisasubsetwithnoleastelement,asshowninpartc.1.1.
