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Fall2003 Q2

# Fall2003 Q2 - Page 1 of 4 Math 135 — 008 Algebra Quiz 2...

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Unformatted text preview: Page 1 of 4 Math 135) — 008 Algebra Quiz 2 Time: 40 minutes November 3, 2003 NAME (underline surnameHM“ , W In”- -_______' N o calculator ai‘éowed! 0.0/3.0 e HAM) «f ‘. ‘ -\ F 5 / < *1“qu a e Z). Pageg 0“ Question 1 [7} > “L A}. 1’ Use the Chinese Remainder Theorem to decrypt C = 45 using the RSA private key (49,143). ﬂ: 1% = (03' H 0t l ' ‘1 _, U ‘ . >4: ‘55 M‘ﬂog‘g em {3V ‘9“? 26‘” 1H3 eq/motéxwk 50 Saw v Vie”q (mod. x5) J 4| \t/EVISM‘Q! (moo: “3 \/ M Mod \“5 H53 61 EM Eé (mod \3) *9: @501! by Femm‘j LHM ”9mm. 1+5“; 1 (mod r5") ‘ ‘- ‘2 ..... ‘r r r‘\ 1’3. \ §ﬁ ._ l/‘(DHc’E éMq;(é\L§{ ‘6‘ 1‘L18 '7' at»; ‘ (W‘OL J. )é/M E \v“ 6‘ L: E 6 (mo d 3‘} M mod. z\ H53 \ (mam mac, bx/ @acmoexs LLﬁ—tée."3¥\1-\\ LIB'bs—umod H3 , W? 2‘ m 2 M ‘ ‘ ‘ ‘45 - ' 5w {WNW "a, J m ¥ 6) r - m Q m ' .- , ms - gowe XE éakmo‘i; K3} ‘5’ ‘4’ 3 “mod “3 1;. ” gram (9 X: 6* Sq ) (e7? ivy: m smes 64 Ox :3 \ (we M 1“”: ”" ”" £7 M 4c Zr =3 *QC mo i H} ‘ 2E7 2V5: 6(mod H) gmce Hrgofwd‘ﬂ . 3; ~ 1/ \ ‘ ’ 3: 4&qu \O‘,’ Mggedmﬂ f~ ’ t \S a. so\ ‘0 5A4 {6 “M28 —é\:-2;1 up: \$34 , t \l + at: K : 5* \“SL M3 ' 2 ”J; \4 3(‘5 K5716 ’3 338’ (ﬁg V 7&2 \isg 3‘45 (meé NS) . "/ / . 1A - A A s< ML (Anro 02‘ {4% é: {W3 Page 3 of 4 Question 2 [6] Write out a truth table for the following statement. . P OR (NOT Q .—_—=> R). (g Page 4 of 4 “J Question 3 [7] The sequence (11,0.2, - -- of positive integers is deﬁned recursively by (11 = 1,0,2 = 5, and an = an_1 + 2an_2 if n 2 3. Prove by induction that if n E P, then an = 2" + (—1)". § \ -J Vroyw W? :p: o=\ <1 0:1 ‘EC _, ~ \ \ “v” . €83 \$1 + (“‘5 LS: 6A 1 \ \/ :1 \ ( EV 09% ‘ﬂ 3 \Q __)l 3%“ ‘5“! W1 SMkm—mm Awake nz‘x n, V. R5». 3 ‘ J: we} S 1 : V: +\ L “gag" , f“ 3, = x :5 J “1’13 UN WM") , . ‘ \ , : /. ‘7. che 3:33: we gg-mfrg‘ggxtgmﬁvv \5axboﬁrme:~£;ur n~ @Aeawmeﬂka SWRm-CM TS 4mg ~Qr \4; r” .4,- ‘9 @ ﬂow? ’XCUXQ ,Jgev n: Kg—H amen“ *~ Mew w, dew?) > on « ”MM : 8%; (43k #ng + (4\H] [EV assw‘AQJ-WOV‘) :2“ f MEL»; 9: air—kw 2‘ (“GM ;, W siren‘resmM, is Xxx/ﬁe go? 0 2km. when EWFW £5 Jae Lav @y m dwﬁ‘on )WQ 3 bannJ 4 ‘5 Awe e; an m e? V/ ...
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