COMP 547: Assignment 1 Solutions

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233691878922252066348509134604244471333546312317852220895508\ 369427626913772850143760176143129931451424429293884759562490\ 322601317396442135442907921311723452332263114970776692997399\ 86) 5471234567920 is not in QR_n (root of zyx: 14610868789133624\ 475555226176467004479669770506607128074264943715736115077162\ 010446302281624600501359713324371970059657445871355106003774\ 678727964187749344888565217585386682960440817674026518833688\ 7) 5471234567921 is in QR_n (root of x: 75025271047767905533581\ 412636736474619870006210493607454026925709136635761964424525\ 780560454922479800157513998513109146131267147121907977627943\ 9668991248196886208816906104469457020877946309152705431) 5471234567922 is not in QR_n (root of zyx: 30812163795597324\ 468796688894991268686404825263879572098525789607706678269048\ 973733779536806399235445240579782920828038971648803553499375\ 219885677685297660079194110297518594536232466939364065688775\ 3) 5471234567923 is not in QR_n (root of zyx: 13056387703305225\ 554037691119354300482091241579335424697456809789537706376662\ 359381011261909204392563098928526888103454707911882594778920\ 148121815199371458543851407561254753027368916918296277277248\ 93) 5471234567924 is not in QR_n (root of zx: 303878112073435188\ 395185499250644611897322927992088655497461296287060382259962\ 142124003695556370860099531962708007476760763195505959119974\ 412892446112838905911059584014213022816726355456791667636250) 5471234567925 is in QR_n (root of x: 57309927544358819123985\ 694018979093115486392253387043463977624513784616574134137384\ 703833837248541010757190319876296764149678236234058948990851\ 5712510445465032540986337774653266411763044620727261102) 5471234567926 is in QR_n (root of x: 14207001819992942465395\ 303445331802249333659443911413486906619977794458803788310190\ 303175737195055886454332971366135001838790395921222294497979\ 67656151745559006271162802952823587058348067743185313643) 5471234567927 is not in QR_n (root of yx: 530330182538695748\ 333843401788714361595729951249979169454216657307030484588210\ 419540224406633343710956552045187771900944602273222399321263\ 18
389253605405939855060913257019569382985851949618610552765743) 5471234567928 is not in QR_n (root of yx: 681756156107811742\ 568091019091746720835660796932371665230986310276155529438383\ 880532771695254615399398651378677983340589259418496954263595\ 096128490110042461280509220051830319965029276293520091009633) 5471234567929 is in QR_n (root of x: 13899318648628341004431\ 748460597502287488889889805364067722479443471455998030499553\ 148402846946069834085524443328580685416948548290787287598816\ 07279637921952695115994458766792287648893040402863612633) 5471234567930 is not in QR_n (root of yx: 661918933924162757\ 857527606660903356751260704646876208859300924011334350017154\ 130406705701446263764558835957741901143551758941607260202948\ 268088877296293611771517973114797777025024325407506029194456) 5471234567931 is in QR_n (root of x: 12665621260243823565330\ 411286464795235951931214166642099785450597553287939601235290\ 133260213998837331706548294622947237360232975286367476221921\ 9673286808711472914133656876983941248408571059925693734) 5471234567932 is not in QR_n (root of yx: 142761112601125263\ 574680860246888870245952180960859652463627264992350400629142\ 735991845837467765361513385863336647884012850692358136634292\ 329258364414974689121659907807822816185358698483029763623072\ 8) 5471234567933 is in QR_n (root of x: 10781496633616684872793\ 411669508296032100054408011354164084315309554648387190623061\ 850391562678286948882357840252083624802721634805404252819442\ 97663116531448042598341239325818399793043374538401395006) 5471234567934 is not in QR_n (root of zx: 101323748526877060\ 118429211893238272588270321557227335538218007473353883271196\ 406674890000364557523433762502208167432017112953001862798243\ 604063408172337779240626851851569811070727283206777476975339\ 0) 5471234567935 is not in QR_n (root of yx: 119132793044056803\ 802525804982885990372882971613104284242242208181988239023522\ 343734725910885821817345053226507229172681037610344462807077\ 708929408034477497740906941987063785113099116233528322639990\ 8) 5471234567936 is not in QR_n (root of zx: 996976662065957545\ 19
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: 17819930918348761695484963068116150
Page 21 and 22: 5471234567945 is in QR_n (root of x
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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