COMP 547: Assignment 1 Solutions

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561857978871574450994255621219475283040175070738448443032696\ 922347826900704881854987371429914498131786185423365931997315\ 931426018093182160579080630407695664470774522049047255070929) 5471234567937 is not in QR_n (root of zx: 127314487993111225\ 919875105223364055928864409640824418920283666850313186305080\ 251159547105628289641393841787394376076721189893723955526246\ 146397669116063903525596855512340874513292682935957623859968\ 4) 5471234567938 is in QR_n (root of x: 93236433381740928305820\ 135585733137526581297468655865852627417824469737349861291856\ 325296058762323316290456265727807745554809437023466312856571\ 3646142468346056767516916966652689530963648025713236525) 5471234567939 is in QR_n (root of x: 97087300755223112895532\ 918316464460824380572380122221027368014350825286544315920758\ 011719417198403369620199314569375548544205100890953480306149\ 4868170010638107576476766082861745150377077078246514802) 5471234567940 is not in QR_n (root of zyx: 12709327186073049\ 392281974269135794323432863815715191979745058534628227288862\ 169273470242451379657965177337826704553682629478397786876914\ 149067461970812932208274585491785675903722340154565312667611\ 54) 5471234567941 is in QR_n (root of x: 15491443895590091464179\ 014805031332970464457652728729538091328834936117057727108137\ 003157812669217292865665736928687260645071304543233487395424\ 01110413552951807960453528948523807630401547469065442128) 5471234567942 is not in QR_n (root of yx: 322628261872906683\ 243137727664297199302547354960745939497192483897998010085920\ 865420178641425129305044456333635709879513699790291879603370\ 864665394481419567526986888610756599016374594415579740214733) 5471234567943 is in QR_n (root of x: 84644393471355361366593\ 637906474031131934900814123552993931019651568497322417036893\ 242589006250108793027467215823486078196991423958203601101156\ 4272946694321215941204662649206748460983744841704400375) 5471234567944 is not in QR_n (root of zx: 150149041432966600\ 639100201058136637397149137967951687497819053652606958365901\ 793540235966947667172567392254485020492588462902087436412464\ 542396464581891118960551422319438890173957076119830888990623\ 8) 20
5471234567945 is in QR_n (root of x: 56933623937542874302042\ 629168843714381450205482599012992640358448772963693596851899\ 996610246171248068392699988057408416104159671055426912144904\ 1558992092901496910873991646011154442186549065546540953) 5471234567946 is in QR_n (root of x: 83943580235744031615328\ 069345678444618580023604821395569552681604215386943465587170\ 961840584225221874996780702611222540562641864692354443024324\ 0253864336246785979637784432031217896547337690126842839) 5471234567947 is not in QR_n (root of yx: 754216630642513299\ 684062180718543822975346624493475763142431269429338523663141\ 383541788300794335626172810999586100038474388383976758759912\ 798164832114626763055687989403194835588816200901494586849671) 5471234567948 is not in QR_n (root of zx: 838139542465648623\ 835549963076815676033748839624585003463859546253549994432063\ 867021775971596431106129937272321621073197601159128108579716\ 563967313747602443978592813541871211926730058182947000244124) 5471234567949 is not in QR_n (root of zyx: 12428532921251207\ 806019187313692654151091317117306318321669553466842451905942\ 552316777848104813627502494889019291825085178327935329722314\ 582084895481501371402616116308332726216695876613173503861937\ 83) 5471234567950 is not in QR_n (root of zx: 145715770990666028\ 018763396135041426659957645364534839565375795615319909788615\ 167940292136091419474881534761565790196071379694669793983507\ 425771142730615562998609686119465726562365762875274343555567\ 3) 5471234567951 is not in QR_n (root of zx: 109986181129242322\ 715424209110821956345727347837765759438558445411981124759104\ 987814156115111822624945919896215813961601891684382905821188\ 190211250806021887324976221642299324376627400133852527758477) 5471234567952 is not in QR_n (root of zx: 124487139352334906\ 719707391661237304832632478801577776150494406521852583601538\ 701538927318643222182695477685297198452165626795018225696072\ 4717326861601545927572098988867560174386406662152066170991572) 5471234567953 is not in QR_n (root of zx: 148544504346167008\ 476375132468434104896139792021536376076882600021091742607010\ 412948767868031355659492466554550651426135097700902977390835\ 21
Page 1 and 2: COMP 547: Assignment 1 Solutions Oc
Page 3 and 4: + x^277 + x^276 + x^275 + x^272 + x
Page 5 and 6: g := x^997 + x^996 + x^994 + x^991
Page 7 and 8: We know that the distinct powers of
Page 9 and 10: + x^790 + x^788 + x^784 + x^783 + x
Page 11 and 12: The following Maple function comput
Page 13 and 14: a:= 0; b:= 0; while not (a = -1 and
Page 15 and 16: 21284645683965405414161580243440656
Page 17 and 18: 17819930918348761695484963068116150
Page 19: 38925360540593985506091325701956938
Page 23 and 24: 5471234567962 is not in QR_n (root
Page 25 and 26: 5471234567979 is not in QR_n (root
Page 27 and 28: integers in X fall into either of t
Page 29 and 30: There are simply too many condition
Page 31 and 32: (a + √ x) p−1 2 (a − √ x) p
Page 33 and 34: Thus, if rootLV fails, then a does
Page 35 and 36: Now, armed with these lemmas, let u

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