Ly Thuyet Mat Ma

7/24/2019 Ly Thuyet Mat Ma

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TRNG I HC BCH KHOA H NI VIN IN T - VIN THNG

H Ni, ngy 17/02/2016

BO CO L THUYT MT MGing vin! T"# H$n T%&ng T'(n'

NHM 2

1.H M!NH "#C $T "TTT%0& $'( 201)0*(7 2.+HM MNH TU-N $T "TTT%06 $'( 201)&)2( ).NUYN NC TN $T "TTT%07 $'( 201))&&6

Chng 2 H thng m ha c in (Classical Cryptosystems)+34ng 55 8 9: 99 ;5 ?@ iA 9: ? ;D =E =3F9 Gn ;IJng


2/64

;I:ng K; 9 K. TI:ng 934ng ny 9ng ; KP =Q 9R5 =Sn 8; K n ;i >8R; ;V 8; ;Wn =3F9 K Xng 9Z yS ;I39 K[ I =\i 9Z 8y ;]n. N^ng >;ng 8E @ G yS =A =3F9 K Xng niQ i>n ny, =_9 `i>; ai 8y;]n ;bi c d 9Z 9ng ;


3/64

ihi 8E =3F9 ;[9 i>n `kng 99 9yAn ;Ie bi ` a ;I] la 9 gung =A ;x8iA 8 ;S n: =A =3 99 a ;I] ;Ie bi.By gi\ 9ng ; =3 I ;xn ng 9ng. NS `bn ?


4/64

lCJn J9 8; 8 qqinp c % c l8:X 26.w] X, =A 9: v * a v 2, ax aRy 9ng ;9 ai *c 2. "3 `hnIj `V9 ;3 n3 lv7. N@ =3F9 8E @ =Sn *.7 2 v 6' 1) lM:X 26, =@

9^ N. Xng 99 9V9 nng ;34ng ;[, 9ng ; 9@ =3F9

q q i n p %C w w + M.L8 ;S n: =A 9ng ; gihi 8E NS 9ng ;9 ai 99 9:n K F5d 4n8:X 26, 9ng ;


5/64

8:X 26, 9ng ; 9 9fn cp8 c|; a gi^ 0 a 2'. : =@, 9@ 12%26 v )12K[ [ 9Jn 9: 99 5]8. HEy nxn a: 99 99 9


6/64

;34ng Vng 8i . wx aRy, 8; ;x8 ?iS8 =fy =Z ; ;ng 8R; 8E ny niQ ng3\i 9: n;:n, 8_9 XD B``gp a $K:X =E ;A i>n 99 =A ;Wn 99 8E @ 8; ap9;:I, 9Jn n3 K. "f ;in 9Jn 9iQ Xi?@, a] X, 6. =@ 9Jn 8; ap9;:I 9Z 99 ?]9 ;39 ny 9@ 89 99 Kngyn 0%2', a] X ? v l21,&,2,1*,1&,17. ;3\ng ;x ?@ ;34ng Vng ai 8; ;m9@ ng Xz n. TI:ng ;I3\ng F5 9Z 9ng ; ;ng 5 ;9 a: ;[9 ;S ;V ;bi ?


7/64

;I3\ng F5 ny, G. C9 5n ;]9 8R; 8E K Xng ;[9 ;S fn ;V nW; ;bi;I:ng ;iSng n nun ;in 9: 99 ;fn K 99 9^ 9i ?


8/64

L3 d Ikng ?9 ;x8 ?iS8 99 9; ?, 9ng ; 9@ i K[;IDng F5


9/64

9: =Sn ny. NS 9ng ; ;iS5 ;9 9: ;:n ` `hn 8E, 9ng ; Ko

Cng ; 9@ n^ng K[ ;IDng F5 nW; 9: 8; K[ ;y =i 9Z '. N3 9ng ;


10/64

C9 ;V =:n `n =f ;bi L v p 9by a: 99 aWn =Q a] X, v ? a v c 9@G 9: a % ; 9@ ;fn K G ;W5. T34ng ;[ n3 aRy, w v p a % p X3\ngn3 ?n,?iA8 ;I n@ `kng 99 K Xng n@ =A gihi 8E. N@ KP =3F9 Xz Xng =A ?A 9: XD=@ 9]n c9.

TI:ng a] X 9Z 9ng ;


11/64

":bn ny =3F9 Wy ;m 8; `i aiS; ngun ;I:ng 9ipn;iqi9 8pIi9n,55p8L!!! pn; l1*17/01/27, ;Ing 61. M; \i gihi ;]9 ngun gJn aQwigpnpIp;R; ;:n 8E @ =3F9 =3 I, a ;n 8; Gn=iA8 n3 =i ai n nin 9Z [email protected] ?i ;iSn ;i 8; 534ng 55 ;V i

9: ai>9 ;x8 ?iS8 9x ?@, 9ng ;9 9yAn =i : 9Z ;


12/64

2.. ,m 3i5m cha 3ha 4 C6ch th:c th: hai.

TI39 S; K Xng 99 d ;3eng 9@ ;I39, 9ng ; =3 I 8; gihi 55 ?9 c9=n =3F9 9x ?@. 3\ng n3 8 ai>9 ai 534ng 55 =@ 9@ 5fn ;; 4n

gihi 55 =f ;in ;In n^ng 8 ;in ngun, 8_9 XD n@ 5 ;9 niQ 4n 8;9; ;]n ;:n.

Cng ; KP ;iS5 ;9 8 ai>9 ai w e ;In. "A ;x8 ?iS8 yS ; 9Z ;m ?@,nn ng =S8 9^ 9i =f ;in, ;V 6, ;V 11, a ;I] n3 ;I39 a =_; a: 9ng;I:ng 1 ap9;:.w v l 0, 0, 7, 1,1,2,*,0,1,(,(,0,0,),&,',2,0,),6,',1,0,1,0

l ={ ;in gi a: K ng I 9Z , ;V 2 =3 I K ng I 9Z B, aa . NS

9ng ; 9i `kng 67, n@ ;ng 99 9^ K =S8 =3F9, 9ng I ; =3F9 8;ap99;:I v l0,0, .10&', .01&*, 0.2**, . , .01&*, 0 /HEy ng aQ 9 ap9;:I ny cW; i>n. Tm ?i 9ng ; `iS; = Xi 9x ?@ ', ;V nW;, ;V 6, 11, . N^ng ;m ;I:ng 8R; 8E =E X9 ;W; 9h 9Dng K 3Fng. ln3 9ng ; KP ;Wy =:bn ngun, J =E X9 ;W; 9h 2 . Bei aRy, J 8i ;h 8;99 ng nin Wy 8 9Z `hng 9^ 9i ;iSng n. TW; 9h =E X9 `kng 9DngK 3Fng. HJ ;3\ng =3 I ap9;:I , nn gfn =ng ap9;:I , e i gy I 5|5

X9 aQ 5] yS ; =f ;in 9Z 9x [email protected] =Q `y gi\ c9 =n =3F9 i, nu9 bi ap9;: i, r n nW; ?i ivr. a cW5 c `kng i, nS 9ng ; 39 ;]n r ai 0 r 2', gi ;I 8E nn chyI ?i rv!, =y Khn 5{8 X:;.

.02'0, .0)*1, .071), .0)((, .027', .0)(0, .0'12, .0)01, .0)2',

.0&)0, .0))(, .02**, .0)&), .0&&6, .0)'6, .0&02, .0&)&, .0'02,

.0)*2, .02*6, .0)26, .0)*2, .0)66, .0)16, .0&((, .0)&*

i ;I n nW; ;V ),9 ;A .071), =@ gi = .2 , C: nn 9ng ;39 9mng 9i ;V nW; X9 2, n@ ;34ng Vng ai 9x ?@ 9Z `hn Ij C, HEyK Xng 9Dng 99 ;V9 =A ;i8 I ;n 5fn ;V ) 9Z 9x ?@. Cng ; KP;iS; R5 1 ap9;:I 8i K Xng _5 i 9Z 9^ 9i ;V ), (, 1) . Cng ;cS5 ;n X9 ap9;:I ;I39 =y

v l0. .01'2, 0, .0&'&, .0&'&, .01'2, ..., 0, .01'2

hn 5{8 X:; .i ai 0v iv2'


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.0)72, .0267, .0)*', .062&, .0&7&1, .027*, .0)1*, .0'0&, .0)7(,

.0)'1, .0)67, .0)*', .026&, .0&1', .0&27, .0)62, .0)22, .0&'7,

.0'26, .0)*7, .0)22, .02**, .0)6&, .0)72, .0)'2, .0&06

i ;I n nW; e =@ gi ;I ;V & , 9 ;A .062&, =@ ? Gh 4n9,,X,p,K n3 9x ?@.

L3 d Ikng XW 9W8 Khn 5{8 n nW; n 4n K: ai n^ng ng3\i ?9;I:ng =ng ?A 9h i ;I3\ng F5, ax aRy 9ng ;n ny a3F; ;Ii K: ai 99 534ng 55=f ;in =3F9 ;Ixn `y

Ty nin, 534ng 55 =f ;in Xz Xng 4n niQ =A 8 `kng ;y.Tbi K: 534ng 55 i>n 9]n c9 4n ng3\i =f ;in "A 9@ =3F9 =F; Khn 5{8n, 8; K ;I:ng n^ng gi ;I n 4n ;I:ng 9@ =A 5D F5 ai

99 gi ;I n 4n ;I:ng 8; i.TI:ng 534ng 55 ;I39 =@, 9ng ;n ny ;[9 i>n =iQ ny ;W; 9h ;I:ng 8; `39."A ;@8 ;u;,=y 534ng 55 9: ai>9 ;x8 9x ?@. ih K 9ng ; =E =E c9 =n eXi ?@ ;.

:I i v 1 =Sn n, 8 n3 Ko

1. T]n 99 ;fn K 9Z 99 9^ 9i e a ;I] i 8:X n, a 8 ap9;:I2. C: rv1 XSn 2' ;]n .r.

). HEy =3 ?ivr0 =A 9@ gi ;I 8c 9Z .r

Cx ?@ 9@ P ? , . , q9n

ng n^ng > ;ng 8E @ 5 `iSn nW; 8E ;y ;S. N@ ;3\ng =9 XDng;I:ng 89 9 = ;I:ng 99 ;\ `: 9i ;fn. ngyn ;u9 IW; =4n gihno Mi 9^

9i ;I:ng `hng 9^ 9i =9 ;y ;S `ei 9^ 9i ?9 l:_9 9@ ;A 9Dng . C]nc9 4n, 8; 5|5 :n a 9Z 2.& MR; 8E ;y ;S


14/64

M; ;I: `hng 9^ 9i =9 9Jn a Vng Xng ai ; n^ng a] X 9Z 8E ;y ;S. C9 8E wigpnpIpa Hi lcp8 89 2.) a 2.7 ;x ?


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!OOT++!$!!BwLw!wYNHU+wBwM

wBO!COBHHBBN!w+HB+N+!

M; ;fn K cW; i>n =3 I X3i =y l 9@ 2'0 9^ 9i ;I:ng =:bn ;


16/64

C^ 9i ;3\ng ;I39 p a iS8 ?i =Vng K n@. "iQ ny 9: ; ìS; IkngNv

$S; F5 5 ìSn nW; ;. : =@, Bv;

i^ n^ng 9^ 9i cW; i>n niQ, I a K 9~n bi, 9ng 9@ ;A `kng ai w:_9 8; ;I:ng a , wx I g|5 9_5 ai niQ ngyn 8 a K g|5 9_5 ainiQ 5 8 4n nn ; ;Wy w 5hi K a I ìA ; 9: :_9

[ ?S; F5 In nn cW; i>n niQ 4n nI a cW; i>n niQ 4n , axaRy X[ =:n 9Z 9ng ; vI a vn

T 9@ ;A ;iS5 ;9 5n ;]9 a c9 =n Ikng v: l9 d Ikng ;: niQ 4n :;, !v! a + v [ 9Jn ;]9 F5 nW;. X: =@ ; c9 =n n^ng X[ =:n F5d 9: )(2 9Z 2'0 ?d ;[ ;I:ng =:bn ;


17/64

:q ;p g:apInpX ;; spnpapI ny q:I8 : q g:apIn8pn; `p9:8pK

XpK;I9;iap : q ;pKp pnXK i; iK ;p Iig; : q ;p 5p:5p ;: ;pI :I ;:

`:iK i; nX ;: inK;i;;p nps g:apIn8pn; ying i;K q:nX;i:n

:n K9 5Iin9i5pK nX :Igniting i;K 5:spIK in K9 q:I8 K ;:

Kpp8 8:K; i?py ;: pqqp9; ;piI Kqp;y nX 55inpKK

2.* ;"t m thay th54

M; ;I:ng n^ng > ;ng 8E @ 5 `iSn 4n 8R; 8E ;y ;S. N@ 5

`iSn

=3F9 K Xng ;I:ng 5fn 9 = 9Z p `: 9i ;fn ;V, a] X.

C9 ngyn ;u9 IW; =4n gihno Mi 9^ 9i ;I:ng `hng 9^ 9i ;y ;S `kng8;

lH:_9 9@ ;A ging n ;3. C]n c9 4n, 8; :n a 9Z `hng 9^ 9i

=3F9 [ 9Jn a 5 Xng 9: 99 an `hn g9. TI:ng 99 ;Ing 9 =, n^ng

?


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8; ;y ;S 8R; 8E. My 8un ;y, Bpn In?in `iS; 99 :n a

=ng =3F9 K Xng, X: =@,


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Bhng 2.2o Tfn K 9Z f S; ;3 ;3\ng g_5 ;I:ng ;iSng n

niQ8 ;in F5 d ;V ;bi =bi Xi>n 9: p l8_9 XD B 8; ?h nng ?9.

N3ng n^ng gx aQ 99 9^ 9i ?9 Cng ; 9@ ;A =:n Ikng, B, , , !, w,, +, N,

ai 9@ P 8; i ng:bi > :_9, 9@ P ging n3 ;, , :, i, n, K, , I

;p: 8; ;IR; ;[. B ; 8; K ;fn K =4n gihn ?


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C9 ngyn 8 , i, : 9@ c 3ng ;In n. NS 9ng ; nxn a: X~ng ,

9ng ; ;Wy Ikng ?


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?d ;[ ;I:ng an `hno

Tbi ;\i =iA8 ny, ?iSn ;V9 aQ ngn. TW; nin, 9@ IW; niQ 5}ng =:n, a gih ;yS; ?9 n 9fn=3F9 ; ngi>8 9: =Sn ?i 8; ;I:ng 99 9


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2.9 8R; 8E @ Xizn I e niQ n a[9 ;I:ng an J9, ;I:ng ;9 5{8 9ZXgI pn :q HpnIy K8:nX, pK wpInp l w:ygp ;: ;p Cpn;pI : q ;pI;, nX g; CIiK;ip lTp :I K5p9;K.

=y 9ng ; ;@8 ;u; 8; 9 9y>n ; a 9Z I;I C:nn :yp, 8 ;p:99 ny, pI:9? H:8pK =E 5< `y K[ ; ;ng 8R; 8E. Cng ; ?n9n, ;p: =@ 8; K[ ?@ iA, a 8; 9;

;Iy>n ;@8 ;u; bi `kng 8R; 8Eng Hi;:n Cì;;, ng gfn =y =E 93i 9[ J9 Kin 9Z 8xn Kip +;Ii9?,gi ;3 =i>n ; 9: pI:9? H:8pK. TI:ng =@ 8; 8{ giWy ai xn hnng3\i =ng nhy 8 8 n

B ngy K =@, 8; ;in nun ?9 c; i>n

Cì;; K: 9|5 ;W; 9h n^ng 9i ny gi 9: H:8pK, ng 8 XDng i ngy K=@ =A ;]n ;:n. BW; ng\, H:8pK nhy ?}i gS, Ij Ing =ng ;b: ;S 5~ng ;Z.ng Wy nn 9@ng gi `V9 =i>n ;]n Xi ;i i =@ a K =@ 9\ =Fi, n@i ai;K:n Ikng J 9@ ;A KP ;i ;8 Cì;; a: ngy ;iS5 ;p:. N3ng i ngy;In ;]n, a K =@, 8; ;3 =Sn ;m Cì;;n3ng ai ni Xng ;in nun ?9


23/64

H:8pK ngin 9V a n@i Ikng J 9fn =Sn iXing T:I5p Mn:I K8 nW; 9@;A. M; ;\i gin ngun K =@, i 8 9Z `V9 =i>n ;]n 9Z H:8pK ;i, aH:8pK n@i Ikng aWn =Q ;Ie nn ?{n 9W5 4n. $i H:8pK a ;K:n ;i nC`i;; a:


24/64

Ikng npy KP ;i 8; ; n^. TR; 9u9 9un, npy K8 cW; i>n a ` 9hnK; 9~ng ;y. TI:ng ?i 9\ ` gihi =i, 9 ùn l n@ 9 =A ;[a>, 9 8E @. NS ap 5 a > ;ng 8R;8E 9Z i9p , K =@ ap 9@ ;A ;3\ng cyn gih ;b: i9p ?i gi: ;iS5 aiB:`. Hng I: n nin 9ng bi =iQ ny IW; Gn ;IJng.n ;~ 9: `pnpy niQ n8 =A ng aQ aWn =Q ny

Ng3\i =J9 9hn gi9 9@ ;A 9 d Ikng 9ng ; m 8; ]; ?i gihi 8E ;in nun.BiA ;3Fng ging n ìA Xizn 9^ w ;I:ng NpapI a 9^ + ;I:ng +Ip5Ip."iQ ny 9@ P X: i in =E chy I ;I:ng 8i 5in `hn 9Z ;9 5{8, ù; =fai `hn in =f ;in =9 9


25/64

=8 :in; 9fn XDng ? ;R; i 9]n c9 ;I:ng K[ 9yAn ;hi 9Z J. TI:ng;[9 ;S, 8; ai i =n 8y =ng nn =9 XDng 9Dng ai f S; 8Ji `hn X[;h: 8E @

2.=. 7lay$air m"t m +>?@A+yqiI a 8R; 8E =9 K Xng ;I:ng 9iSn ;In ;S gii ;V 2 èi ng

n a ng "V9. wi n^ng ;i 9{n i>n =bi, J 9@ > ;ng ? yS, n3ngbi n [9 ;R; K[ =A 5 a n@

H> ;ng +yqiI =9 5; 8in ?:hng n8 1('& èi CIpK p;K;:np, ng=E =_; ;n > ;ng ;p: ;n 9Z `bn 9 =A ;yS; 59 9]n 5Z XDng n@. T8 a: ai>9 n@ =9 XDng ;I:ng 9iSn;In ;S gii ;V 2,n 9~n XDng n@ ;I:ng 9iSn ;In B:pI.

Cx ?@ 8; ;m, a] X, +yqiI. N^ng 9^ 9i =9 _5 bi KP ` :bi `}, =A 9@;m 5yqiI a n^ng 9^ 9i =9 gi^ bi =9 XDng =A ù; =f 8 ;IRn ' c' N^ng?:hng ;Ing ;I:ng 8 ;IRn =9 8 =fy èi n^ng 9^ 9i 9~n bi ;I:ng `hng9^ 9i, ai ! a r =9 9:i n3 1 ;mo

ih K =:bn ;


26/64

. NS i 9^ 9i 9Dng ng, ;y ;S 9^ 9i =@ `kng 9^ 9i ngy `n 5hi n@,ai 8 ;IRn `J9 Gn ;m 9; 9i 9Dng ;i 9; =f ;in. w X, 8p ;Ie ;n

. NS i 9^ 9i 9Dng 9;, ;y ;S 8i 9^ 9i `kng 9^ 9i ngy `n X3i n@,

ai 8 ;IRn `: Gn ;m ng 9i ;i ng =f, a] X : ;Ie ;n w":bn ;


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$S; Gh 9Z `39 =f ;in

.

H4n ;S, =y 8R; 8E ;y ;S =9 8 gih. B39 ;iS5 ;p: 8 ;ng K[ 5V9;b5 n =ng ?A, 9Jn 8; ;m ?@, a] X pin. i ;n 9; 9Z 8 ;IRn `kng99 9^ 9i 9Z ;m ?@ a =_; ?S; Gh 9Z `39 =f ;in a: 8 ;IRn ?9

By gi\ cS5 bi ;V ;[ 99 9; =A ;n 99 9; cS5 ;p: ;V ;[ ;I:ng `hng 9^ 9i

Ci 9Dng, =:bn ;


28/64

;]9 8R; 8E ng +5 p:IgpK +inain a BIp X CiIp, ng 8 9@ ;A gihi8E 8; 3Fng =ng ?A ;in nun 8R; 8E

e =y 8; ? ;R; =9 XDng. ih K 9@ i =:bn ;


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?i `hn 8E ;34ng Vng. C9 ;R; ;:n 8E @ +yqiI ;bi 89 2.6 8; a] X=4n gihn 9Z 8; ;R; ;:n 8E @ ?i, ax n@ 9@ ?i i 9^ a 8E @9ng =A ?i i 9^. M; K[ ;y =i 9Z 8; ?] ;[ 9Z 8; 9_5 `hn Ij KPn e `n 5hi

5|5 nn nn `n ;Ii KP 8ng bi 8; d ;yS; ;34ng ;[ a gih8 8:X 26o


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: =@, 99 `hn 8E . lT[9 ;S 99 9^ 9i =f ;in an ?n ng nin n@ ?


31/64

TI:ng 99 534ng 55 9ng ai 8; 8 ;IRn n c n, 5 a 99 an `hn =4ngihn a: ?i n ?d ;[ a ;y =i 8i ?i a: 8; ap9;:I 9Z n K ngyn gi^

0 a 2' K Xng v 0, ` v 1, ..., t % 2'. w] X, ai 8 ;IRn M n3 ;In, gih K`hn Ij 9Z 9ng ; o

`:9?9i5pI

"iQ ny ;Ie ;n l9ng ; ;8 8; c =A =iQn a: ?


32/64

`hn. By gi\ 9ng ; 9@ 99 `hn 8E, 8 ;S n: =A 9ng ; gihi 8E "4ngihn 9 9fn 5 a `hn 8E ;n 99 ?i 9@ = Xi n, ;y =i 8i 8; ap9;:I,a nn ;p: R; ai 8 ;IRn ng9 =h: N. TI:ng a] X 9Z 9ng ;, 9ng ;9@o

B v l17,1,2' !% l1 7 ,1 ,2 ' v l7'',&27,66 v l1,11,1& v `,

a ;34ng ;[ 9: 5fn 9~n bi 9Z `hn 8E.

MR; 8E Hi ?@ =A gihi 8E 9 K Xng 99 `hn 8E, n3ng n@ ?


33/64

TI:ng ;I3\ng F5 ny, 8 ;IRn ng9 =h: 8:X 26o

T =3F9o

wx 8R; 8E Hi Xz ` ;Wn 9


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[ nf8 n 9@ ng ?@ ?


35/64

Bhng 2.' C!!

w 9 9fn 99 9^ K 0 a 1. w] X, 110.101 ;I:ng > n 5n =bi Xi>n 9:2' 21 22 1 l`kng ') ;I:ng 94 K 10.

Mi gi ;I 0 :_9 1 =3F9 gJi 8; ì;. M; =bi 3Fng 9iS8 ( ì; =3F9 gJi 8; K (%ì;, :_9 8; `y;p. n nW; 8 ( ì; 9@ ;A ìA Xizn 2'', a K

n nW; 8 16 ì; 9@ ;A ìA Xizn =3F9 6'')'. Tn X3i Xbng n 5n. C@niQ 99 =A 9@ ;A 8 =iQ ny. M; ;I:ng n^ng 99 ;i 9{n =3F9 gJi C!!, aiS; ;u; 9Z 8pIi9n ;nXIX C:Xp 9: ;I: =i ; n3 ii a . Bhng 8E C!! 9ng 9W5 9: 9ng ; Xbng

ìA Xizn n 5n 9Z 99 ?] ;[, ?] i>.Ty nin 9ng ; KP ? ;ng 8R; 8E ?


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;


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9R8 =i ai f S; 89 =]9. Cng ; 9ng 9@ ;A ;b: I 8; ` =S8 pigpIa =S8 9@ `: ni nW5 9; 8 n@ ;[9 i>n ;I:ng 8; ?:hng ;\i ginn}, gi 0 nS 9:n K ny 9n a 1 nS n@ . C@ niQ 99 ?9 nn4n n3ng ?


38/64

C9 :np%;i8p 5X a niQ Vng Xng 8R; 8E ?9 y 9f ;Ixn ;[ ì; ngnin. TI39 ?i 9ng ; 9@ ;A K Xng 8; ;R; ;:n 8E @, 9ng bn n3 lC34ng & :_9 lC34ng ', n@ 9fn ;iS; =A ;b: I 8; 9i ì;ng nin =A K Xng n3 9x ?@. M; 99 =A ;b: I 99 ì; ng nin

K Xng ng nin ;[ nin chy I ;I:ng `hn 9W;. w] X, n^ng ;iSng nni>; ;m 8; =i>n ;Ie `n Xn =3F9 ìS; =Sn 8; ngn ;; 9Z K[ ng nin.Ty nin, ging n3 R; =ng ;iQn =A Khn cW; 99 ì; ng nin KP ?n ;[ nin ?9=h8 `h: Ikng 8; ? ;D ?n ;I:ng 5fn8Q8. Hf S; 99 8y ;]n =Q 9@ 8; 534ng 55 =A ;b: I 99 K ng

nin 9@ Kn 9: ng3\i XDng. wx a] X, ;3 ai>n C 9{n 9@ 9V 8; 8 InXl 8 ;b: I K gih ng nin gi^ 0 a 6'')'. 8 gih ng nin ny 9fn 8;=f a: a Khn cW; 8; ì;K;Ip8 =f I. C9 8 InX l 9V9 nng a niQ> K gih ng nin ?9 =3F9 X[ ;In > 9:ngIpn;i ;ySn ;]n. M; >9:ngIpn;i ;b: I 8; 9i 99 9:n K c1, c2, , ;} 8En

cn v cn%1 ` l8:X 8 .

C9 K cG b; ging `n =f, ;I:ng ?i n^ng 9:n K , `, 8 ;8 K 9i

5i 99 8i Gn >. wi>9 K Xng 99 > K gih ng nin X[ ;In >9:ngIpn;i ;ySn ;]n 5D F5 ai 89 =]9 ;[9 ngi>8, n3ng =3F9?ySn ?]9 9: 9: 89 =]9 8E @. "y èi ax J 9@ ;A X[ =:n l;R89] nS 99 ;


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8; a] X, 99 > ;b: K gih ng nin 8R; 8E ;I:ng ` 9 ì; gih ng nin, 9~n =3F9 gJi > 9_n `R9 i. TI:ng 934ng ;Ixn ny, ng3\i =f ;in ;b: I i K ngyn ;n 5 a G 9h i =ng X3 ai ) 8:X &. Cng ; =_; n v 5G a 9Jn 8; Kngyn ng nin c =@ ; 9Dng n ai n. "A ?ei ;b: 99 8y 5; =i>nBB, ;iS; R5 b; ging `n =f =A c0v c 2 l8:X n. C9 > ;b: BB ;b: I 8;9i 99 ì; ng nin ì, èi

1. cr vc2r%1 l8:X n

2. `r 99 i; Gn ;IJng nW; 9Z cr.

T] X. "A 9: 5 v 2&72&62&67(*2&6*7(7 a G v )*67)6(*&'67()&'(*(0),n v *7((&701&0(')1107*&16((''217&1)71'7(1*61.

LWy c v (7)2&'6&7(((&7()&*01).99 =f a: `n =f c0 v c2 l8:X n

v ((&'2*(710&7(7(00*70(**177&6010122(6)172.

C9 gi ;I 9: c1, c2,...c( o

c1 v 711((*&2(11)1)2*'227&'*62&''&*(12)(22&0(

c2 v )1&'17&60(((((*)16&1'1)(01'206070&'1(227

c) v &(*(0077(2)071'62))2722))1(''7&(**&)0)''

c& v)*)'&'7(1(*)'112*22)&70*)'&61(*672)10)(*

c' v 67'0**'11'100*70&(*01761)0)1*(7&02&60&0c6 v &2(**1&(2(7717&01))'&61*06'(266'1'171)26

c7 v &&)1066711&'&)7(260(*0)(6)(''*)(17'2166(

c( v 7))6(7612&1*'0&6)*7&1&2)')))67'00')72&)6.

LWy ì; Gn ;IJng nW; 9Z 8i gi ;I ;I:ng K ny, Xz Xng ;[9 i>n

`kng 99 ?iA8 ;I cp8 K y 9n, ;b: I 99 9i

`1,...,`( v 0, 1, 1, 1, 0, 0, 0, 0...


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C9 > ;b: B8%B8%` IW; 9@ ?h nng ?n ;9 = 9Z n@ =A ;I]9 cW; 99 ? `i; Gn ;IJng nW; 9Z cr.i `kng ? :g2 :g2 n, =iQ ny 9@ a 8E @ n ;:n.

2. ,!y5n tRnh Stin phPn hTi #hi$t UVng 3W #eX!ences

L3 do TI:ng 5fn ny, ;W; 9h 99 =ng X3 8:X 2.

TI:ng niQ ;xn ng in Gn =Sn 8E @, 9@ 8; ipn > gi^ ;9 =

a n nin. NS i 8n 8; 8V9 = `h: 8R; IW; 9:, ;x ;9 =J ? =3F9;IyQn =i, ax aRy ;9 = 9Z 8E @ IW; Gn ;IJng. M_; ?9, n nin ? ;i 5; ;ySn ;]n = Xi 8o

cn8 v 90cn91cn1 98%1cn8%1 l8:X 2,

?i 8 99 > K 90, 91, 99 K ngyn. NS 9ng ; 9 =n ;I:ng 99 gi

;I


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c1,c2,c8

=@ ;W; 9h 99 gi ;I ;iS5 ;p: 9Z cn 9@ ;A =3F9 ;]n `kng 99 K Xng ;i5;. C9 9i ?S; Gh 9Z K 0 a 1 9@ ;A =3F9 K Xng 8 9x ?@ =A 8E

@. C ;A, aiS; Ij 8; 9i 99 K 0 a 1, K =@ ;8 8; K ì; ;]9 F59Z 9i 9x ?@ =A 99 `hn Ij 8:X 2, ;mng ì; 8;. w] X, nS 99 `hn Ij 1011001110001111 a gih K 9x ?@ =3F9 =3 9: ;I39, 9ng ; 9@

l`hn Ij 1011001110001111

l9x ?@ 0100001001011001

l`hn 8E 1111000111010110

ihi 8E =3F9 ;[9 i>n `kng 99 ;8 99 9i 9x ?@ =A 99 `hn 8E9]n c9 ;p: 9Dng 8; 99. M; Fi ;S 9Z 534ng 55 ny 8; 9x?@ ai ?:hng ;\i gin n 9@ ;A =3F9 ;b: I K Xng IW; ]; ; K 1,0,1, 0, 0 =p8 bi 8; 9i 99 gii =:bn )1,ax aRy 10 ì; =3F9 K Xng =A Khn cW; )1 ì;. N@ 9@ ;A 9: ;Wy K[ ;i 5;

cn)1 v cn cn)

a `W; ? ap9;:I `n =f ?9 ?


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"y 8; Fi ;S n 4n 8; 5X 8; ;\i gin, n4i 8 ;:n ` i ; `i;5hi =3F9 gi ;I39. +34ng 55 ny 9@ ;A =3F9 ;[9 i>n IW; Xz Xng ;I:ng5fn 9Vng K Xng gx =3F9 `iS; =Sn n3 8; ;n gi ;:ng ;in 5hn ilL a IW; nn. TI:ng Hxn 2.1, 9ng ; 8< ;h 8; a] X 9Z 8; ;


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0v 90.1 91.1 lnv2

wiS; X3i Xbng 8 ;IRn o

C9 ngi>8 90v 1, 91 v 1, X: =@ 9ng ; =:n Ikng K[ ;i 5; cn2v cn cn1. TR; ?


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;]n ;:n nn 9@ng 9: ;Wy Ikng =y ;I3\ng F5, 8 9ng ; =E ;x8 ;WyK[ ;i 5;. Txn xn 9ng n3 K. "A ?iA8 ;I 9: 8; K[ ;i 5; 9Z 9@= Xi 8, 9ng ; gih K 9ng ; ìS; c1, c2, ...,c28 +34ng ;Ixn 8 ;IRn o

Cng ; ;Wy Ikng 8 ;IRn 8 ng9 8:X 2 ?i a 9 ?i ?9 ;x8 ?iS8 99 > K 9Z K[ ;i 5; IW; Ij Ing. ihK 9ng ; ìS; =3F9 100 ì; =f ;in 9Z ?@. "i ai 8 v 2, ), &, ..., ;m 8;IRn 8c8 ;I39 =@ a ;]n ;:n yS ; GyS; =n 9Z 8xn. NS 8; K in;iS5 gi ;I 9Z 8 0 GyS; =n Xmng bi. C9 8 9i 9Dng 8ng bi 8; gi ;I?9 ? K 90 ,98. =@ 9@;A ?iA8 ;I cp8 9i =@ ;i 5; ny ;b: I 5D F5 ai ;Ixn ;[ 9Z ì; 9Z?: ?


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Ti 5; ny ;b: I ;W; 9h 100 =iQ ?i>n 9Z ;Ixn ;[ `n =f, ax aRy 9ng ; 9@9 ;Ih \i =ng, ]; nW; X[ ;In n^ng ?iSn ;V9 8 9ng ; 9@.

ih K Ikng 100 ì; =ng e gi^ 9Z 8; K ;Ixn ;[, a 9ng ;n 9ng ; ;[9 i>n 8; K i XW, n3ng n Ikng9ng ; =ng 8:X 2, X: cnvcn a cn( v cn(. "A nv16

c16v c17c20 c2& v 101v 0

TiS5 ;9 ;p: 99 ny, 9ng ; c9 =n ;iS5 c1', c1& . ....,c1. By gi\9ng ; 9Vng 8in ?S; Gh 9ng ; ng.

[ R;. C: c1, c2,c),. . . =3F9 8; 9i 99 ì; =3F9 ;b: I èi > ;i 8;;ySn ;]n 8:X 2. "i ai 8i n 1, 9ng ; Eyo

"A N 9iQ Xi 9Z ;i 5; ngun nW; 8 ;b: I 99 9i c1, c2, c),. =@ Xp; lMN v 1 l8:X 2 a Xp; lMn v 0 l8:X 2 ai 8Ji nN.

Bkng 9Vng. "f ;in 9ng ; 9@ 8; ai nRn c|; aQ = Xi 9Z ;i 5;.M; 9i 9@ ;A =5 Vng 8; 8i Gn > Xi ) n3 cn) v cn2 % Ij Ing K=@ 9ng =5 Vng 99 8i Gn > ngun n3 cn1 v cn l]; nW; 9: n 2. Ty

nin, 9@ n^ng 99 ]; Ij Ing Ikng 8; 9i 9@ ;A =5 Vng 8; K[ ;i 5;9Z 9iQ Xi ]; 4n X[ ?iSn. w] X, Ey cp8 c|; Gn > cn& v cn) cn1 cn. ih K 99 gi ;I `n =f 9Z 9i 1, 1, 0, 1. [ ;i 5; 9: 5|5 9ng; ;]n ;:n 99 =iQ ?:hn Ko 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1. N@ IW; Xz =A;Wy Ikng =5 Vng 9i cn2 v cn1 cn.

NS 9@ 8; K[ ;i 5; 9@ 9iQ Xi N a nS n N, K =@ 8; ng 9Z 8;IRn M n =ng X3 8:X 2 ai K[ ?S; F5 ;ySn ;]n 9Z 99 ng ?9. w] X,nS ;i 5; cn) v cn2 cn, ;x ng ;V ;3 ;ng 9Z ng =f ;in a

;V `. : =@, Xp; lMn v 0 l8:X 2 ai 8Ji n N.


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By gi\ gih K Xp; lMN v 0l8:X 2. =@, 9@ 8; ap9;:I ng ?9 0l`0,`1 ...,`N%1 K: 9: `MN v 0. Cng ; ;Wy Ikng =iQ ny 9ng 9W5 8; K[;i 5; 8i Gn > 9: 99 XEy c1,c2,c), a 9iQ Xi ny 9Z 8i Gn > n} 4n N. "iQ ny 8 ;n ai gih =n Ikng N n} nW;. M ;n

ny 9@ ng Xp; lMN v 1 l8:X 2. "A K[ ;i 5; 9Z 9iQ Xi N o

cNnv90cn .9N%1cnN%1

"i ai 8i i 0, Ey

=@ Ml0 v MN . Mi Gn > ;i 5; 9@

=@ 9; 9i 9Dng 9Z Mli1.Bkng 99 [ 9Jn `, ; 9@ `.Ml0 `.MN. ih =K 9ng ; `iS; `.Mli v 0 =i ai 8; ai K i. =@

: =@, ` ;[ 8 8W; 9; 9i 9Dng 9Z Mli1. wx 9; 9~n bi 9Z Mli1 999; 9Z Mli, 9ng ; ;Wy Ikng `Mli1 v 0. Cng ; 9@ =3F9 `Mliv 0 ai 8Ji i0. C: n 1. C; =f ;in 9Z Mln%1 9@ gi ;I

`0cn`1cn1`N%1cnN%1v0


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wx ` ? =A 9@ =3F9

2.2 C! U4TiS; ` 8E @ 94 gJi 8y I:;:I =E =3F9 5; ;IiAn ;I:ngn^ng n8 1*20

èi 8; K ng3\i. C9 ;; nW; =3F9 ìS; =Sn =E =3F9 ;iS; ?S èi I;I9pIìKa ;Ie ;n 8y nig8 ni ;iSng =3F9 K Xng èi ng3\i "V9 ;I:ngTS giiCiSn !!.N@ =3F9 9: =iA8 ;;p8 IW; n ;:n a 8; K ]; ai 5b8>;ng =E ?S; ;9 ;I:ng ;W; `bi. Ty nin, 8; n@8 ` 9Iy5;::giK;K BLn,MIin prpsK?i, HpnIy? ygK?i, a pIty :ty9?i, =E ;n 99 5 a5in `hn =f 9Z nig8 ;I:ng n^ng n8 1*)0. ? ;R; 9Z J

=E =3F9 ;


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L, M, N 99 9n Gb;. TIn 8; 8_; 9Z 8i I:;:I =3F9 26 9 =n =i>n

= 9 in b9, Ku5 cS5 ;p: 8; a~ng ;I~n. 5] `n ?i 26 8D cn%nb5= 9 in b9, 8; fn n^ Ku5 cS5 ;p: 8; a~ng ;I~n =A 9b8 a: = 9in b9 9 =n 9Z

I:;:I iQn ?Q. Bn ;I:ng 8i I:;:I, 99 = 9 in b9 9 =n =3F9 ?S; ni ai

= 9 in b9 ~ c: 8; 99 4i ng nin. n^ng ?S; ni

?9 n e 8i I:;:I. Mi 9n Gb; 9@ 26 ;iS; R5 `n =f 9@ ;A.

;Ing =h: 9iQ. N@ 9@ 26 = 9 in b9 ~ c:, ?S; ni ;I:ng9_5.

$ `n 5]8 a ging n3 8; `n 5]8 8y =n 9^

5g`:IX. N@ 9@ ?:hng K 9_5 9u8 ;V ;bi 9@ ;A =3F9 K Xng =A ;I:=i K 9_5 9Z 99 9^ 9i.

$i 8; 5]8 =3F9 nWn, 99 9n Gb; =f ;in N a~ng 1/26 9Z 8; 3F;. =@, `u; =f ;m 9x ?@, =i>n =i G , K =@ ;


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n. C9ng3\i gi 8E @ ;5 `kng 99 gj ;In `n 5]8 a gibi;Ixn ;[ 9Z 99 9^ 9i 9 =n `ei 99 `@ng =n. K =@ `hn 8E ny =3F9gi ;ing3\i nRn, ng3\i :bi `hn 8E a: 8y. TIxn ;[ 9Z9^ cW; i>n ;I:ng99 =n ;5 `n =f. "iQ ny 9@ ;A =3F9 cp8 n3 K. "n a

5]8 =3F9 gun a: 8; KFi Xy Ku5 I 9Z 5g`:IX. "n a 5]8 =3F9 gun a: 8; Xy Xn ?9 Ku5 I 9Z 5g`:IX. NS 5]8 =3F9 nWna =n i Kng n, K =@ 9:n =3\ng =i>n G 8y 9ng =3F9 ?S; ni =n =A 9x ?@. H. : =@, nS Gn ;IJng =E =3F9 |5 ;y a: =@, K =@ 8; 9x ?@ KP n Kng. d Rn ;34ng ;[ 9: ;Wy ;V ;bi ?


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5n ;]9 ;W; `bi ;m a~ng c:y 9Z 9n Gb; ;y =i K[ ;y ;S 9:

8i ?d ;[ 9Z ;in nun.

wx aRy, 8 ;S n: =3F9 nig8 ;Wn 9


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`hn 8E. wx 8i ;in nun K Xng ?9 n;IJng =iA8, 5n ;]9 ;fn K ?9.

Ng3\i nRn 9 =4n gihn K Xng 99 ;iS; R5 ng ngy ;m 99 9:Xp`::? =A

gihi 8E K 9^ 9i =f ;in 9Z ;in nun. ng K =@ ;iS; R5 bi 99 9n Gb;=Sn a ;I] 9 `kng 5]8 nun gihi 8E a ;iSn n gihi 8E ;5.

wi>9 K: 9Z ?@ 8; K[ ;IF gi5 ;y>; a\i =A 99 5n ;]9 8R; 8E. gih ;iS;;In 8; K ngy `bn 9_n 8; K ;5, a, :ng =@ fn ;V ` ;bi 9@

`n =f K 9^ K =yo

X8Ga`n a:n5y

59q8GTW; 9h ;I:ng K ny =3F9 8E @ ai 99 ;iS; R5 ng ngy ;34ng ;[ ;m 999:Xp`::?.C9 8E @ =f ;in ;34ng Vng ai 8; ;;i:n 5pI8 9Z 26 9^ 9i

9ng ; Ey gJi 5pI8 ;;i:n ny . TI39 ?i `V9 ;3 ;V i =3F9 8E @,8; 9n Gb;

`iSn, ax aRy ;3 ;V i K Xng 8; ;;i:n 5pI8, gJi n@ B. ;34ng ;[ n3aRy,

9@ :n a C, , , 9: & 9^ 9i 9~n bi. 9iSn 3F9

nxn a: 99 Khn 5{8 , B , a C .

Cng ; 9fn 8; ai 9


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5pI8 ;;i:n ;V e `hn = X a, a 5, ; p I s, aa, a K 9^ 8;

a K. NS 9 ? ;3\ng ;9 I\i l9@ ng ?


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B v l`qGap:8 lr5 Ks itIn l c; l9gy lX l?

C v l`ai?;r gq9Gny lXtIpcs 58 :.

T5 9Z Gh 9Z 5g`:IX l?i =ng ;iS; R5 =3F9 K Xng K =@ 9 =4n;fn 8; 8R; 8E ;y ;S, =@ 8; 99 Xz Xng ` gEy. +34ng 55 ny


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=E 8 ai>9 9: =Sn ;ng C]n n8 1*)(, ?i 8; K =i 534ng 55 9Z99 5]8 nun ;InK8 i;;ing =E =3F9 ;n ; =f ;in.

2. Y&ercises

1. CpKI 8n Ku5 cS5 8; 99 J5 `] 8R; ai MI9 n;:ny, :_9

8; ; Ti`pI lK


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niQ 5]8 9@ ;A ; nS 9ng ;9 8:X 2*

(.ih K Ikng `bn 8n 8E @ 8; ;


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8:X 26, ;W; nino

B BBC.

ih K `bn =ng n@i ai 8; ;V ; 9iQ Xi ?@ 1, 2, :_9 ). ;V ;bi i 9F

9iQ Xi 9]n 9@ P 2, a c9 =n 9]n c9 KW; n nW;.

12. NS a a s i ap9;4 ;I:ng ? 9Z +fn

2.),

X:; Khn 5{8 G n nW; ?i i v 0.

1). C9 `hn 8E Y!M =E =3F9 8E @ `kng 8; 8R; 8E ai 8 ;IRn Hi

Tx8 `hn Ij.

1&. C9 an `hn 9i5pI;pc; =E =3F9 8E @ `kng 8; ;R; ;:n 8E

@ ai 8; Hi 2 c 2 8 ;IRn. C9 `hn Ij =3F9 gihi GyS;. Tx8 8 ;IRn 8E @M

1'. ap `u; 8y 8R; 8E Hi 9Z B:`, ;I:ng =@ K Xng 8; 2%`y%2 8 ;IRn

M 8:X 26. C< 9 gung 8; 99 ;Wn 9


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8E @ 8 ;Iic =3F9 ;8 gi a: ai>9 ; ;R5 99 ?d ;[ 9i 9Dng

9Z `hn 8E lcp8 9i M9 2.7.

ih K 8 ;IRn =3F9 K Xng 9: 8; 8 ;IRn 8E @ ;I:ng 8; Hi

94 yS. Tx8 i `hn Ij Ikng 8E @ =A 99 `hn 8E ;34ng ;[.

1(. C: , `, 9, X, =, p 99 K ngyn 8:X 26. p8 c|; 99 ?S; F5 K =y

9Z Hi a 8R; 8E qqinpo "bi Xi>n 9: 8; ?i `hn Ij 8;

9_5 lc, y 8:X 26. C9 `hn 8E ;34ng Vng ln@, :_9

M< ;h 8 ;S n: =A ;[9 i>n 8; 99 ;Wn 9;ng ny

lwi 89 ;i ;x8 I 9x ?@ , `, 9, X, p, /. Bbn nn n@i Ij

n^ng gx `hn Ij `bn 9Jn a 8 ;S n: =A 59 i 5]8.

1*. M; 9i =3F9 ;b: I èi 8; = Xi ` ;i ?ei 001110. Tx8`n yS ; ;iS5 ;p: 9Z 9i

20.p8 c|; ;Ixn ;[ ù; =f ?1v1, ?2v0, ?)v1 a =3F9 c9 =n èi

= Xi ` ;i 5; TIxn ;[ ny 9@ ;A

9ng =3F9 =3 I èi 8; 9iQ Xi i ;i 5;. 9 =n = Xi i

;i 5; `kng 99 ;iS; R5 a gihi GyS; 99 534ng ;Ixn 8 ;IRn ;]9 F521. ih K 9ng ; cy X[ng 8; 8y L ;V ;bi 99 9 K C: a C1


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Tx8 99 > K C0 a C1.2). w: gi^ n^ng n8 1*(0, 8; Ghng 9: ;yAn Xng 9: N =E ;iS5 1

`ei 8; ;I8 OK e =f ;Ing. C9 an `hn =E `u; =f Bbn =ng ;x8 ?iS8 8;

::g:. Tn y ;m 100 n8. M; ;iS5 ;p: 100 tpI:.

"S8 2& gi\ 8; ngy, `bn KP 9fn 120 n8 =A =b; =3F9 8; g::g:.

Hi ?iS5. T


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lL3 do "i ai > ;ng l9, 99 gihi 55 5 ;9 IW; niQ a: ;[9 ;S

9^ _5 =i _5 bi 8;, 9V ?


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lp8 5 9 X3i ;n Yap.

2. C9 `hn 8E K Khn 5{8 9Z 8; ;R; ;:n 8E @ 9yAn =io

L9psrtnnt8ayyI8t

Bkng 99 ;[9 i>n 8; K ;fn K, =:n 9]n =3F9 K Xng ;I:ng 99 ;R;;:n 8E @.

Xng 8y ;]n =A ?iA8 ;I gih ;yS; 9Z `bn. ; gihi 8E

an `hn ;


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9y;:Kinp, gninp, ;y8inp a, =@ cy X[ng 94 `hn

?i 8E N a N. $S; F5 99 9^ 9i , C, , T ai

99 K 0,1,2, ), ;34ng Vng

l Xng ;R; ;:n 8E @ 9yAn =i ai K[ ;y =i n 1, 8E @ K =y

9i 99 n9p:;iXp =3F9 Wy ;m =f

niz8 Ku9 ;A ng3\i ;V 83\i `o

TTCC C C C TT C C C TC C MT TCTCT C T.

lB wiS; 934ng ;Ixn ;V e ;[9 i>n 8R; 8E qqinp ;In n9p:;iXp

`hng 9^ 9i. N^ng bn 9S ny 9@ ;In 8R; 8E qqinp

7. =y =E =3F9 8E @ K Xng ;p: 534ng 55 wigpnpIp K Xng 8;

Gn ;IJng 9Z 9iQ Xi 8; ; nW; 6. ihi 8E n@ a GyS; =n s 8 ?


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:`q gGg9K 98 gt;:pX9 KXp iX5`;8: a5 ip ? iq5 i8 qn : 8a5Gqcp r K8

c85g?99y?;Iqt5ycI;psI8s?`àg;ga;pq r: X qp q? a 5 c K g IK : Ia g

;r` K tIt? i8 : gpXpqnKs 8 I9i95a:g5Xnq5?;XìKIL n

5Kryp;99ppK:XI?s :;i?Ì:GIXq8 tgg9pàgs 9XGcg5`gGs 5`

Xy::GX8`XGg8yspi?8aKsIanGKtX8g:GK?85KGq:Ia;saXq9

rt a g K: : G K 9 r? ` IKp a ` p

+ 9 X3i ;n 9sy. C9 `hn Ij ;m Tp Xapn;Ip

: q Mpn n9ing 9Z iI I;I C:nn :yp.

*. =y =E =3F9 8E @ `kng 99 534ng 55 wigpnpIp. ihi 8E n@.

lC9 `hn 8E =3F9 3 ;I^ ;I:ng 99 ;R5 ;in 8y ;]n ;hi aQ lcp8

+ 9 X3i ;n c?r.

c?rI:s85catn5i8à`Gr9n:s9599aaq aKq acti;yc:cG:r

cpctc8yrGqB;ni9X?`c?nrGiX5GiGq5`59iXKa9i

s`p;`;cIrnIKn9iaqqca:?rrKs8GqarsrKXyr:grcX`:c

r;95t85i8`tca::Xy`qXK?cgGqXK?cncpKI:rGq5q?nX

Kq aiI;Gq I5s r IKtcg5q ; r GiynIcnyn;s89?r q ìItK8pK r

By:nXXttn;t85iIsn8s8aTiIy:n;à8s

10. =y 99 `hn 8E 9Z 8; 8R; 8E Hi

iI?t:5rr:5;q5qXIG

K Xng 8 ;IRn


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11. C9 ;Ixn ;[ K =y =3F9 ;b: I `ei 8; =ng ?d ;n =f ;in 9Z 8; Khn 3Fng L. Tx8

> K 9Z K[ ;i 5;.

lTIxn ;[ =3F9 3 ;I^ ;I:ng 99 ;R5 ;in 8y ;]n ;hi aQ lcp8

+ 9 X3i ;n L100.

1). C9 `hn 8E K =y =E =3F9 ; =3F9 `kng Oing Khn 3Fng L

ai `hn Ij


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ih K `bn `iS; `u; =f Ij

Tx8 `hn Ij. lC9 `hn 8E =3F9 3 ;I^ ;I:ng 99 ;hi

qip 9:8 5;pI lcp8 5 9 X3i ;n L011.

Ly Thuyet Mat Ma

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