COMP 547: Assignment 1 Solutions

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867610908415254416831766577282279084646008699895257082242172\ 948757661588040299072160443888243660954746439296997997910209\ 2) 5471234567971 is not in QR_n (root of zx: 411059193912748192\ 956549957434744433876973198054865887641137010371644572269672\ 745836607053372131550552612004845823465553187682822368466044\ 947716132772867340175154069149253239964172418060278954069548) 5471234567972 is not in QR_n (root of yx: 118730808754480106\ 897847085659016045490649273788082429157325795427468836081538\ 613845470507920039809552096161090176712501390342829053591625\ 548645505061484505198836567597939769727175305569821949207005\ 7) 5471234567973 is in QR_n (root of x: 11282034450832219025337\ 421940210911612850100620192499008735663992492416629944850476\ 279717911747532247234102863448836207213242178169492622358020\ 44083914794700721361533642326475251869184428783568498314) 5471234567974 is in QR_n (root of x: 15726516054906273846796\ 285339178450835013592400057564053622617178469038742590918062\ 429298741510619347125104525023725909853200400602329408931224\ 48793381580136663780265788193663634177388241839424113792) 5471234567975 is not in QR_n (root of zyx: 92172498476720587\ 297729575803354102900137738266967964153587712536798941054539\ 195139710839958113204336587543164893127031187304527691421905\ 518518718976372841903688640254083974006275485389714323438581) 5471234567976 is not in QR_n (root of zyx: 12179630545870818\ 024652563023712374478672009205281727043860907373728825957868\ 076856945410034351265397706475532650654527980900003700914959\ 938499271155159808927004416042295693796964634401260063471435\ 03) 5471234567977 is in QR_n (root of x: 39613924233577612145036\ 837452859763270278074018310278146839895809140324895619886455\ 323291812832131460325668771137144733681094380124809958877498\ 2967223043571649935876941786441759051029747233299732099) 5471234567978 is not in QR_n (root of yx: 515807452241340486\ 133800569413085512053304021085029997470017322809136631794917\ 898260428980069134905151947664696044949474183498660150942111\ 20526676024351428534573114198457724607171885434642109602964) 24
5471234567979 is not in QR_n (root of yx: 881414167435764925\ 734017446611796949413843138542333463408018632234840655090084\ 167793981800293941200545122680281860678163571266704138033767\ 088824216998913375003555782633996440227608638240793329108829) 5471234567980 is in QR_n (root of x: 27682281899428262436182\ 729012317441675924168023406270819294566585079331392609257538\ 755813553703964922942299005414865028981363205075026688193026\ 4587240482964322354825415822357118582816959532225231739) 5471234567981 is in QR_n (root of x: 89113675414809781874531\ 020349592726385551440107170136882368987234729251336629564152\ 459393208412429436189893118688899920184293431498632895220115\ 3275109594740482430634599837326891880893610720187435305) 5471234567982 is not in QR_n (root of zyx: 28923188287494486\ 155814137623053769901988801817198786810047094545511742129222\ 704153274607896326742172603295736218524930304188226247499569\ 171161122208835591556829908422261559239037807266897278051747\ 3) 5471234567983 is not in QR_n (root of yx: 598609656671634698\ 270028756793599281064869983015527141911940705475341988265341\ 747601498943476186801173436894897243158600431086032438432151\ 827960888296883252952910474335889484286491640215073135915377) 5471234567984 is not in QR_n (root of zyx: 66484772945823830\ 331417391499168741858777546020354434935375816699435892227934\ 018309725363714851602421156111525086550842875391096861117245\ 262008845243097646616563832995506737511392749323560655146931\ 1) 5471234567985 is not in QR_n (root of yx: 554936448879847414\ 035209433950166745794844725896246171745524946030444743029356\ 157968654157103030054472695677741951986447005469665438226326\ 575999203343317985406991598000039438642794340137531690822147) 5471234567986 is not in QR_n (root of yx: 861370778464761931\ 867587491989043035831300828201284703376101540778985062936569\ 391968367848454376296350574872597052804957670228205973341344\ 828518183544124544870470226582882446253177216791243701804280) 5471234567987 is not in QR_n (root of zyx: 41583722403503050\ 091939482603987739556121810868552142326684295941945686992554\ 573367873668797866728487855893858808753285663486061314796012\ 140358673444596816895559689839563635606754300470333640611878\ 25
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 and 20: 38925360540593985506091325701956938
Page 21 and 22: 5471234567945 is in QR_n (root of x
Page 23: 5471234567962 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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