. Khi Kr, K2 đu d6ng, tac6 ul s: ulP vd'
NGUY BIEN a
a
Ua
7vr-n "Nhi torin hoc nhi"
2'-n-2s .4;7 s+ d"a ,ot^ r ^ 6ch6:Gidsftpld4p lu{n-sai.'^a
p phdi chia h€i cho m1t sd
nguy€n td ndo db thubc đy pt, p2, ..., p* Thi du
sau dAy cho thAy p = prpz...pn + I c6 thd chia hdt cho mOt sd nguy0n tO ldn hon p, :
p = 2.3.7.11.13.17 + 1 = 510511 = 19 x 26869 56 di c6 nguy
D6 chinh li phin thi du b6c b6 "phr{t minh" tr6n.
t fr c6 nguyticn tr0n vi vi tdc t6c gii gi6 tta ^cria "dinh "dinh li" li" dad6
ninh ctra O-clit vd rinh vo ph6ng theo ph6p chfng minh cria O-ctit vd tinh v0
lpn gua_44y so nguygn td (1nQt kdt qui het sríc dep han cua đv s0 nsuvOn td (m6t kdt oui h,
dE c[ra So fiqc) mT fiin cdi ban cbn irhd t
Ciic ban thdv dAv, ph6p chfrre minh cria O-clit
r "nhh toiin tioc nhí' chi kh6c -nhau drins m6r til
vh "nhh toiin hoc nhí' c
I
I
"brd
(0 < a, b, c, d < 9 (1)). Til gii thi0t bii ra ta c6 :
1000a + 100b + l}c + d + a + b + c + d = 2392hay 1001a + 101b + llc + 2d=2392 (2) hay 1001a + 101b + llc + 2d=2392 (2)
Tt(2)suyra0 <a<2; O<b<3 (3)
Tt (1), (2) tac6
1001a > 2392-9@-99-18 = 1366, suy ra a22 (4)
Tt(3), (4)taduọca=2 :+ 101b + l1c + 2d = 390 (5) Tt (1), (5) c6 101b > 390-9-18 =273 = b23 Ttd6vi(3)taduqc b=3 +llc+M=87 (6) Tt (1), (6) c6 1lc > 87 - 18 = 69 + c 2'1 Ttd6 vi (6) chi xiy ra c = 7, do d6 d = 5.
Sd hgc sinh kh6ng det giii ld 2375 vh
2375+(2+3+7 +5)=2392
V0y sd hoc sinh dat eiei oudc te li 2. dat siii
quoc gia li 3, dat giiítiih li 5, dat giii cta tiu8ng
lit'l .
Nh0n x6t. Hon 100 bii siii eui vd tda soan đu
giii drinẹ G{c ban sau c6'ldi"eiii telt vn siri bni ildn sdrntron duoc nhAn tang phdm : "
Hn NOi z Bii Vdn Dai, Ll To6n, DHKHTN -
UlaG H4ryQi i Bdc Ninh : Trdn BtnhTing, L0 To6n,,THPT NK Hin Thuy€n ; Nam Dinh : N_Syydry Minh Dtc,1141, THPT XuAn Trudng B;
Ngh6 An z NguydnThÁAnh,12Q, THPT Lc Vidr
Thu4t, Tp. Vinh ; Thanh H6a z Trdn Hodi Thu, 9A, THCS Trdn Mai Ninh, Tp. Thanh H6ạ
_ _Clic -b_qn ssu_cqng c6 ldi giii t6t : Nguydn Hodng
Vi€t, 8H, THCS^Le quf- Don, W{uyen euynih
Hoa, l4C, X3, td 72 Dii,h Vong, edu Gid,, Hn
\Qi :_@ l6ng L4a, qg, THCS-TT Tc Tici;My
Dríc, Hi TAry ; Hodng Drtc Quang, 11A, THPT
Dio Duy Tt, Ddng Hdi, Quing Binh ; Nguydn
Th! Cdm Nhung,ldp 8', THCS Nguy€n Cu Trinh, Huong So, Tp. Hue
NGOC HIdN
sfiu TflIt DUilG THUOc UA GtlMPA Hidn do \1d. : Cho 3 didm A, B, C khOns thdng hdng vd.didm p cd:c! Qdu ba didm d6. lrtuÓn dVql tdm dudng trdn n1i ti€p tam gidc ABC bgn can
pfuii mAy ldn ding thudc kd vd mdy l,in d,ing compa ?
Hd : Tbi chi cdn ding thudc kd vd compa cd thdy 6 ldn thaị
Ban Hd đ ldm nht th€'ndo nhf ?
NGUYfiN DUC T{N
(tp. Hd Chi Minh)
23vd "nhd toi{n hoc nhi" chi kh6c nhau drine mOt t& vd "nhd toi{n hoc nhi" chi kh6c nhau drine mOt t&
"h[u han". Tiei thav ! tt ndy lai l]r m6u Etrdt'ctra van đ ilan den ch6 sai cria "dinh lf' ay đy !
NhAn x6t : Nhfrng b4n sau day d5 chi 16 sai ldm
trong ph6p chfing minh "dinh lf", đne rhdi dua duoc cric ph1n thi du drine đ b6c b6 "phr{tinintr" cira "ntri to6nhoc nhfl' duọ c nf,An t4ng ptrdni ta :
Hn Nqi : Vdn A;h Tudn, ltA2, khdi PTCT-Tin DHSP-Hi_NQ| ; T6.Xain Nam, 6F, THCS Giang V6,
Qqan A" Dinh ; Bic Ninh : LuuThi ThuTran{,8A,
THCS YOn Phons ; Nam Dinh : PhamThi Linh Ouy1n. T2lC, truc,ng CDSP Nam'Dinh ; HAi Duons T ir,ii
Quat Hodn,gAl, THCS Chu Van An, Thanh IIị
Khen them bdc ban .' hldng Hai long, 8B THFI NK
Trdn Phi, Hii Phdn! ; BnjVariNshta, S,{ THCS frdn I\,Iai
N-inh, Thanh H6a t N4uy,in U Minh Hodng, vir Nguydn
Qlr"lg Huy,l0 Ctruy0n To{n DH Vinh, Nghd-An ; Ng;ydn Hd Phrong,10 Tod& TIIPT chuy€n Thdi-Niuv6n :Pn"-
Thni Son,lOI, TIIPT NK Han Thirycn, Bdc Ninh.
NGQC HIdN
cHo m.iy prdúl
Trong mQt đ thi tuydn sinh DH nam 1997 c6 bii:
Hdy xnc dinh a đ diong cong y = ? (t-a+4 + i
-3a ti€p xuc voi duon! congy = ? + L MOt thi sinh đ hm bei nhu sau :
Hai dudne cons n6i trone đ bii ti€p xfic nhau
khi vichi kfu PIsau c6 nsfiemk6o : ^
3'(3'- a+Z)+oz -'3o= j.* I (l)
D4t dn phu- r = 3* (t > 0) thi pT (l) c6 nghiQm k6p khi vi chi khi PT s^au c5 nghi€m k6p :
t'+(l-a)t+á-3a-l=0
Didu niv xiy ra <+ Bi€t thric
6 = 1l-a)2 - i1r2-3o-lj = 0 <+ 3a2 - IOa- 5 = 0 5 t 2Ji-o
vul )
a
vi, = 3*, o ien chi c6 siltri a- 5 + 2fi0
th6a mdn đ bei . 3
Ndu ban li gi6m khio thi ban cho bli lim niy
may didm ? Visao ?
HoANG NcuyEN