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graded hw 3 - Math 300, Fall 2011 Homework 3 Due Thursday 6...

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Unformatted text preview: Math 300, Fall 2011 Homework 3 Due Thursday 6 October, 2011 (1) Find the prime factorizations of 218 — l and 221 + 1. V (2) Show that every prime greater than 17 is of the form 18k: + p where k is a positive integer and either p = 1 or p'is prime and p E {5,7,11, 13,17}. For questions (3), (4), (5), let N = aoalaz . ..an_1an E N. Prove that 4|N <==> 4|an_1an, where an_1an denotes the natural number formed by the last 2 digits of N. 1{45) Prove that 8|N <=> 8|an_2an_1an, where an_2an_1an denotes the natural number formed by the last 3 digits of N. (5) Use (3) to deduce that if 4|an_1an then 8l(2 x an_1an). (6) For the following statements, write the statement in symbolic language, deter— mine if the statement is true or false (with justification) and negate the statement: (a) There is a positive integer that is prime, divides 6 and divides 9. P (b) There is a positive integer that is both prime and irrational. (c) For every positive integer there is another positive integer that is at most 2 units away on the number line. ((1) For every positive integer :5 there is an integer y such that for all integers z greater than av, the difference between :1: and y is z. .L “pvlhfiawnmm 6r _2¥“‘-\-— WM = (1." «\XZW'” “146015903 5“ = M514 mm 2m... 3.15; mm 3f5.+\+1 1445”, mi Mu_._ 551x am 520 y Mst Ma Man .{3131 H511. beam. 7\5\—2. .1 Eur “+- 73. "M13 new M2» 5MB Raw 5M2: mm .. Mn 1 M13 “(‘13 "W13. We). \(Mcm 1.21%"? x 612): HEB mm M3. 3‘51?) mama alsma‘ 5Kb=3~Hl “‘42ng Mt. .Blfi\41,mwm 51mm . ‘ Hits-5? . 5%“ new. Ufi- am 3454 . ' 5%3-1‘14 1%? Wm paw mmm 0? 73% = (331 1XI°DL13N - -* gum. momwmo? 1"“+l= 79m“ = (FHXFG'Q‘ 73W13+ W’C‘lfl‘m‘ W15}: 2mm} WM 3r 6mm ‘GESMT’skwwrzfifl 1821.51” 5- mm 2mm mm M? Mam. mmawwm. \Q ‘ mm mmme— 5mm gamma. slum mm ./ usmwm mm Ham “M swim \0 mm Wis: 21% ‘ am mm 3WM 11%: ENE. *~ 1m vim 3:30;“:me s9 11‘+l=[311,q 7» Wm). 1mm zmemwm H4 \s ‘QQ‘WW‘M my" \ m rm»: of [war or velw no! Emu?) m xmmr $0! “#20. \% ya??? M? H 59—: nswx 1e31,,5,.9c.:\u.1?>, n} - Lemma. 2 mm “a. N a H mmwmiw WW my .31 ‘3 @1033”; mg, , ,‘xQ pawn ,Qstm’rfi . m 3:0. ramsfl 3r 1%: z; Mayan) ), 3:3 P=A\3&L*3=_V3{_L9YQQ,&“{P=IW*L|¢18K’§ sr= u ?=L$’\Ub= mm 0 rats: mm? 210% to 485% psmm: qaygrs) %_= [D p” %*)O = 2m 8&5} \ $12 wwm Hahn), $= m Vim m= 161w 4-) MW My Wm Maw Ruby 5M2? I, S= I5 12—- 1%“? 3M 3% WWW awe). sfiQ.z.5,~\_,u,z§1 m2, 14,15,153 33x3 comww MN MW MW. Q WW wmn 3mm“ mysrmxm 32?\.5,°r.\\.7\3‘fl% XM‘KMSH fin, _0 23mm \/ (M. \0. L3. +3. gymsmoyx: gmma 4m 9 Mam am \* is 34mm Hm HUGO = ‘M N ~Warm M10“ W K‘iflm4m _ Tm en-f 19* an thm m. Wimp mum and . dwxmm m H m My” «far \>\ *0 m dwxsml m L\ . -H. mmmgqmmm “UN a ‘24 Satan—m Ms m A\\_®= } 6N; mm %\\_Q“Jeo( menu N: élvfi fih—V‘O * (Sh—1““) ~ w : Wm. ‘ & is Mum M Y \% MMMR“: GMflQMA an '\8 Wm: m ‘3. M amanflam Wfimfis m m mm «SM d: N gm MW 92 mmm my \WMJs‘U No badmme- 5.. mmm: \33; mm cam Jam 9; M We,“ ma. When—m3 \~°< “\QVHQM ‘ 3 we? ., éymém “W . \S} Wmowm mm ‘ m @qumflmmm \ 2*am1n= M e 5;, \s‘mm “hawk. 7m.” (a) . is a wifi “Rog Mu pfiw‘ (Mm mama dmmq 3/ (ix-15%?) (X "KW > 0__ "Mb A MPH 1%. W i=3 :5 . \ 09) min \3 a ’QDSMW Wm?! WM kw \l‘fim am \M‘rmak. _ é ‘ Lk'ieifio‘fi “HT? A 'MIC) Fem. ‘9?th mum Cam? ti \ ‘Ww N Miwlmm v "163%st mmmm \smw‘m asmn‘om \ . (0 W NM pa:ka “my \s 3W 9mm “(my “mks AV wmr TLUMVIS r Wmm mmmsm. “(\EN‘EQ 4d“? 3; (fi’ieisolflwfii‘lox =’X+K \fxfiljlflfl (may 1, Nagam;(wei>owifi>ox _ 'x K. Kwet) ; 5’ mm mm. mm mmpriwwg is :m \Wx mm ‘Sor ¢,\\ may: a \‘ - ‘ . qun chxgigg 1W tum“ \ai. “gym \. (M gimxmengfi- W z>M TMW‘v «M‘ = 103M2ka ll Kfifiei>01flwe£1t=\m-m3\)}gvm) 11 ‘ J: (Mexszsokxm v mm / ...
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This note was uploaded on 04/04/2012 for the course MATH 300 taught by Professor Ctw during the Fall '08 term at Rutgers.

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graded hw 3 - Math 300, Fall 2011 Homework 3 Due Thursday 6...

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