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- Chuyên đề ; ` QUAN HE CHIA HET TREN TAP HOP SO NGUYEN

M2 Š' ngu 2E Và A_ a5} sue 2k}

fo4sneg bị, Tương 4 cx la sa by chia, b Lz Pohl, bs ang, 0 La $8! da

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N& atbs0 ve abeZ, nla so! dW wbidn

Ki chia nt $8 nguy Sin dalteg 6u hop cho n (nod neN) bum ahbe dete 298! de = nhau

+ Méres' doe Disa chia Ait

Pat Ae Bei cae An ilbgl yy tyMelcyiag Ne che die x6" (Qn 40) eas Hoa ke Lên

Asay AWGu chia Yak wha som:

+ Dat Ritu chia Yet cho 2: Wh did Ai Le Do € LOD 41684

+ Dat Riu chia Bet cho 5: Ai SSao fo) St

+ Dat Diu che Ut cho 19: NW: 10es Q.= 0

+ Dar Iau dhe Pet cho 4 va 25: Prche Lat cho 4 We Ga, : 4

A chia fat do 25 bbe Gas 7 25 + Dat Diu che Pat cho 8 SRS Acha Lah cho’ We ara: 8

chin Deak cho 195 Wb Brae: ALS

2% (Dom 3) ke tan cat che x64 cua fh chia VER cho % (Dam 9) t++eetatta ttt » zoo ‘ 5 f N Đ 5 Ấ a os 8

tý : ee & = = > F a) & E° b `: eb B) x 1 Bo 8) AS

<ạ= b(meÀm œ> (a—b): m

+ Mg asthih dak ob dey Arana"?

Cho abcde eZ; m,n CN* the

a) Tle phan a: a=aCmed m)

by We dot wing: a = bCmed m) >b = a (medm) c) TỊc kã6c8X: a = bCmod m), b = c(msdm) > a = Cc (med m) atc = bt+d Cmodm) 4) > aA-C = b- d Cmeà wm) ad Cmew) ac = bd (mod wm) are = bie Cmsd m) ae = be (med m) €) ae b(maÀ mỒ > o*z b"Cmod m3 + are > an = bn (mod mn) ) a= b (mod m > AL kị mm Ỷ XI a= ae dm) h) az b(mod mồ, a= b (med n) => a=+ fro mm) k) ac = bc( med m ) ' (Cm) =1 > A= kmeÀ m \(

Dub OS Format: (Msi! pls las! napus! ae ls õ kl©„|alk jã‡-Íls¿ d6 lai Le lt Gađ b)

Trang 2

b xwuut> khu (a, k3 =1 a ral É he ener = at x qbeNn*™ fr ak = ab abl x M&tss' ea tap Bad Che neN* CNR: (n?+ Sn: 6 Hb

n?+ Syn = Wont Gn = nc -1) + én = @-Dn(ntt) + êm

Vr@-s Dales) tt teb cáa 2364? ahd LEo hip ron 45s lại Ass! chSe 2 2 ve 1% Lt chin Bak

cha à mà (2,5) = = (n-ÙnŒ+1):6 Tử LAI, &n: €

=> (n°+S¡):€ > de

bai 2 Che abcd & N* Điet(a+b+c +4): 6 MR: (ab b+ 2 +A*): G ID

VWz N* daw: nn = n(W'4) = nner (Gath lod 3! wo% 662

ny 455 ba Asé! chris Si bate Tete bea ae oe A Ge “—n):€ " >|@-a)+(#-b) +e 1 +°- Joe ha

kate rb re Wes cect ie wr arbrerdyi6 < go thick >

Wa feb at oP

sai3% Cho a € Z para 6 Chân min Aang: Aang

Jaco: - afa-l) = @-Nalat))

_ G6- goa irk iS ni wiÐ» ibn Kap ron tan Tar A 88 chia Ash cho % va Asa! chica

fet cho 2 wa Q,8) = 1 ie te € 2 Bee a) xí >@-DaG+Ô:e > Apen a-Ùa (a+l

ăô-Ð - ăa°~0(4*'24) = (a- pagan (a 4 +5)

(a= 4) (a- sibafat sp + S(a- Nalarl

= =D (a-Na (art +2 + 5(a-Ðăat1)

sa 2)(a-Dalard (ard) bet cae SS is ay rin ton das Ags! din Dat cho 2, nat

vide Fe ‘sy sấy cí đa lát cha S.MT2,5 wpa emp rou hing 3 mst, tol co 2.3.5= 30 Mw: @-Ya-NăatD(at+z) 130 doc: (Nala): 2d (a-1) ăa+Ð: ® > S(a-Ðăa+1) : 30 (2,3) <4 »>(a"-0): 30 Ciba Jad: aa alat-1) = ala Dla+/) = @-DNalawD@rL)=- A + Tad: a- he: 2 @- Nalan)ji Ss [Ss @-Nala): => A:€ @ (2, 3)=4, 2.326 + \Jn @= Sk (kez) SA:S + Vx @= Sk +1 ">> (@-0(4 +0: S >ALS pe Ble ae tk [SE ek Ss AHS @ Ni (6,5) =-1, 6 S= 30 te â ve đ > A: 30 Vow (°- a): 20 b)(a- a): 30 c)@'Ì- a): 42 bề Tae: aa Wt = Tao: Cx-a”-a = ăaS-1) = ăa* N(atray+L) @- Òala+t[@?=+3(a=3) + (Aa- - 25) |

(-Ðăa+ D(a—3)(a" + 3) + 1(aA-5) Ga paler D

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Bai 4 Chom EN CMR: A= n7(n"- 7) — 36n : SOZO HD Tepe n[ n° (n't) ~ Att = n[n(n=7)-6 |] [n(n 9) +6] h = n(n*~ Fn— C)m< 7a +€ fA = n[m2+1- 3(n34) |[ nỶ-t- 1(x~1)] A= ®(m1)(n-n- €)(n-D(w +) Đ = re I N(aHt)(n+2)(n- 8)(n-L)\(n4+8)

f#-=_ im- 3) Cn 2 (- Ayn (nt1)Cn+L)(n+8 )

AlZ oa T& nen

t Tas ee Li 3, in obi) wl Aoi At cho 4, 2 os lạc c3 KalcÍa 2,

nen fri Ạ 2 2) 4:46 ©

+ Co th tet X hd, 3.96 ngage “6 ký, > > Ag © nin +?

+ TẢ, TẾ aÐ _ `.” Tht 1h dae > fant © oc erie #4: S @ Ea ca ` 3,46 act, k' lây đề SRS 144 = S040 © Tr 006,06 % Aa VU, * Nha, +’ L NON er eat a MM, Ms my, HỘ a + oun here m ` Tie aL Wn Pel a aoe + Pk¿ l2 at

> Kk: ° ab,c,d é |Z |thes màn a +k+tÈ+ 7a”: 6 CME: Lab +c td): 6

=> B2: Che a,b, C, A EN PHI ah+E+rcỀŠ +64 d> :30.CNK : e+k+cx+d : 9O

B38: Che a,b,c © N thea mis at+b+48c : 42 CMR: (T+ b+ 85: 4D Bai 5 Che we N CMR: A= n(m+t)(Fnt+4):6

HD

Tags: | AL =! #w(w+L) (2a +?) = 42n (n+l) + tn(n41) (an +1) Ñ = 22n(wt\)+ ?n(n+1)Ìfn+2)+(a-4) |

A = #n(w+(nt 2) + Tí-Dw(m+LỒ + 42Ăwe1) Co: nữ +1)(n+z)!2

n(n+J) TƯ 3 \ > n(nvy (ate) § 6, toy Mn -lm(m#1Ồ: €

Bi H)-1 25-6 (Co 42:6)

Ant Fh đã se = ua! PEER a> Nh: anr A= O DS n= Sk > A: 5 + 6FA= A => n= 3k3! >Zn+'=6k+3 : => Â:.S +VaelvA= 2S n= B42 > aà+T = 21k +20: 4 =A: 4 Te A:2,A+3w(2,3) =1, 2.%S=6 > #:<€ Đại 6 Ca 2 6Ÿ N dam mụn thea wn: 24m''+1= no CMR: mniS HD x Naw: 5S > mid a Ne mys > (ee 5k#1 => Sa) = @Ủ= 1 (wd) m= Skt2 > mt=(Sk+ 2)" = (+2) = 4 ( maAS) > mm z 1(MeAS9) > 2#m1= 24 = 4@sàS)

> 24wm'+l1 z 5 = O(mAaAS) S 24w+ 1 : 5n :S>n:!5

> mn iS

Cath, khác

» N68 m'5 > ma:5

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+ Nà ví 5 cing br 2,450) % om» mt tS cep bk o> 4 => Zam +d tan cag lS

> Nn nt S2>ni:Ss> mis

+ M8 m toe omg eA S54) 9 D mG, omy LA > ri Fe cay SS Dae Vn cag ES

Trang 4

ba t cls A b ng fee Aekorg sal ceo a+b: lbs | Thane A= ane HD

Gi hp hae pe t WiGyp=2 tro T4 n8 = dG yD V7 a2: a©Š ^ d*(x* 44%) da - 1” +: oy > jay R ân ui Guy) = 4 nen > Hi => r=4 > al=b [LE a > A= a = 42

Bai 8 Cho xy, z le che ss! ng duiong phd bist CMR:

prety less 2k} “hcl Mit cho S(x-yly-H(2-») HD Det a = x~-u ,b=w~ + bh del ta Ade | Z-x = -(a rb) : > >(-)~ z(z -x) = -Sab(a +b), Cán vành) @+k)°- ap by hic he dha Sab(a+b) VA a,b Ee Jace: &+k°-aŸ-Ề - Sa*b + 10áL”+ goảk* + Sab’ Sab (a°+ 2ảb + 2ab*+L3) Sab[(a*+E)+ 2ab(arb) | Sab(arb)(aab'- ab +2ab)

7 Sab (arby(a™+b"4 ab) : Sab (ast)

> (a+b) -aS-b” : Sab( > II

Vay œ-w)P+@—#) + (z~>x)Š dua hal đe 5(-4)WLạ-#)(#~x)

x Cha ! (Gar by> = @rby (arb) = (+b + 20b) (ab +b? 4 Sab + Sab")

- aŠ+ Sa*b +1Ða*b*~ ¿10ả + Sabt + b>) | HH \t Bai 8 Cho sy, 2 lee eae, Sa! nguyen thea man Œ-q93(4~#)(#-x)= x+d+# CMR: Rryr st 2+ HD + Nêu Liy st s6' dé Lac nhai kh: lia cho & the bie so! RY Y- HER Lhe chia bal ho %, ee #rd+% = (O†l+2)= O (mod 3) bai (Cru +4): 3 Đền mại riba Moa vol gd Hk

cáa bơ †e0m

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\)o\ a Àöx có Ảam ned 4

Trang 5

Te ge thiat arbre 9 >| (h2 x1 rc†) 2 2 >|a°+k”rc + E2+0590/-1W lì » > @rbic) > atrbic: 3 & @W+b+c}):4 Nã ả+b”+c? : 3a > +(a+k)(V+c)(c+2 : 3 > iz hay oleate ee ax+btc : ® > abc: & > Thay aS abc ca wit co clea Hà 3 * chi 4: @+b+cXsab+kc + co) = @+byb te)(c+a)) + abc ‘Pai Ạ Chea ib ta cae & SI nguyen CMR: ab(a-b) (ao +b: 30 pe ae Ns œ mguijoo ti (OC = 90) 8 5O That Nậu: x(#!-0 - x(t) (RED) (@x-Òx(Œx+Ð [@ˆ+^)#S5

@Œ-0x(xzt+Ð(x”-4)+t 5(x-0x(xtlÐ

Gn 21; 13%(x+)(# +2) + S(E-Ox(x~+}

Te Œ&-0+ œ+2 la cáạ ® SS’ nga 4#? “rep rin tio dài L” ¡3,1 số : 2 mă2;3)=L

Va La Hy Ge > (@- pate) 6 > SCS Year) +30 @

Lại có G&-2 Po alee +2) lati cua S tạ, RiGn hap vin Yoo tu 196! chia Rat de

5S, As! chia Mabcho 3, Aw! Yat cho2 ma va 2.3.5 - 30

Tn kạ bai bow, ta cd:

dbo (a -LY(ab+b*) = ab(at- bt) = abliat-)-(b*-1)] = b@e—a) - ẵÈ)

Mow ab (ả _L) rrr :| 2Q |> pc»

Baị Che P.4 Le các sS nao ®8' >5 CHE: (PS 42)(p*247) + 1

Ma thổ Larch EA! dled clot se “ở at = 2SkC” 3 _

re Same >a 4 (mod 5)

al- Skl+|2 a - 2k t+ wk+4 da 1

> $6! dL ai a L,4 het 0 “ids L

* Do 4> P.1 PP ~ oe = > P, hcl be p> pla pxr5,a%5 5 p> 4” S ả 1 be 2 x LX (own Net + Ne 4 4` cha ‘his i Sete Sales SaaS aan Ss Do ad sản Getante +4 2S ® ‘Jad: p-q = ¢-) -(4-D

Nre\se ‘S\> S mm prạ Tad: @-Dplpy) le kbar 2 x! Sy

weedy Ass! dil Ne Aim » =(p-Dp(p*): 4 LỆ te > (p-DCp+0: sti ee

do\>S ver phe > p-l wo pri te 256 ion 4m >> A 9s hie Aa 0 VN Pastels 44,

teeta so paces = 4L w EPSP PREP 2¡ Xa M(a”~l): 2#

* Ran net:

+ Mai pÌs sSt ngư 38 oS ti pod 124 > pt =@ ~0Ò(p +): 48

+ Pig rgufe B2 SIẾ pc”: 2R, pt4 c2 >(P-4px4): 28

+_Đ, Kssxw *)Cụ 5 măSj48) =1,5 48- 240

Trang 6

- 240) : 240 a + CMR : a1 : 240 TY 1/44 11,|1 a |~ io tị? ULE V12 lang dept ere + pd 2 thong BS S La pli sẽ Â6Ì giáọ CNK: b dua hết che 2434 HP

‘Do mau cát AZ“ arg et la 23354 ) St 518 Gs M la

Pak Naki = Uns -|= [HE L kl 4 xoá sa cử Taste’ dec 6 nha|- da 2.¡ %;43 ; TỰ 1B

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eight ta tt tae 8111 Ai Ta

Coc $6! rbion We 2 Aec AE ch có dựa vh l|: LÍ se» M: 1 và Hz tử, 46 cay

whan ‘Ning JS) mB voy ca AS! con loi fae ve i £I, LEN, L=L2,3, Tak, do ky 7% H

yien 3a có: (kitke the + key / 1

KỆ

_+

tứ (lạ ch; ki chia Wah cho AS, Uy chio Ad be 1%

Tg le ka M, »

‘De key lert beg + kịp = M T wx XD AT plan 3" gf span y2 Cô: BH L Heyy = 1a

ree dườa hte chia Pat cho ,1%/13 > + Vy claa Đet cÌa