X goila idean nguyen t6 ngu• va chi lieu veil u, u E tich
Ta hay &dug minh dla vac chung cli aa va 6
a,bEI=dA, nen
a = da', b = db' , a', 6' E A.
Do dd d la tide chung cast a va b. Them naa ngu c lb met talc chung cita a va 6, We la cd a", b" E A sao cho a = ca", talc chung cita a va 6, We la cd a", b" E A sao cho a = ca",
b = cb", thg thi (1) tra thanh
Vity d la ubc chung Ion WI& caa a va b. n
He qua. Neu e let mat ubc chung lein nha caa a at b, thi
co r, s E A sao cho
e = ar + bs
Cluing mink. Xet doe chung Ion nhat d rim M de 4. d va e
la lien kit (muc 1), tile la ce mot phiin tit kha nghich u sao cho
e= du
Nhan hai vg rim (1) vdi u
e = du = alit + byu = ar + bs, r = xu, s = yu. n
Dinh nghlit 5. a na b la nguyen t6 cling nhau melt cluing
than I lam lute chung lOn nhdt. Tit he qua coa bei de 4 ta suy ra
B6 de 5. Allu a, b nguyen t6 cling nhau thi cd r, s E
sao cho
I = ar + bs.
He qua. Neu c J ab vet c, a nguyen t6 cling nhau, thi ci 6.
Cluing mink. VI c, a nguyen t6 rung nhau nen theo b6 de 5
ce r, s E A sao cho
1 = ar + cs.
Nhan hai vg rim ding tilde voi b
b = abr + Ms.
Vi c I ab nen c6 q E A sae cho ab = cq. Do de,
b = e(qr + bs)
tdc la c I b. •
B6 de 6. aid sit x Ca mat plain tit Mt khd quy viz a la mat
plan tit bit ki. The thi Mac x I a hoac x ua a la nguyen to
geng nhau.
Cluing minh. VI x la bat kha quy nen the tide cua x la cac
plait tit lien kgt vai x va the phgn to kha nghich, do de met
tube chung kin nhat coa x va a chi S thg la m0 pit til lien
kat via x hoac met phan tit UM nghich. Trong trubng hop thit
oh& ta cd x I a, trong truing hop thit hai x va a la nguyen
US Ming nhau. n
Be de 7. Gici sg x let mat phan tit kheic 0 ea khOng khd
nghich. Cdc menet de sau day, Id twang duang : a) x Id bat khd quy
b) x I ab thi x I a hock x I b.
Cluing mink a) keo theo b). Theo log de 6 ta co hoac x I a
hoac x va a nguyen to cimg nhau. Neu x va a nguyen to Ming nhau theo he quit eta b6 de 5 ta cci x 1 6.
b) keo theo a). Gia sit a la mot itac eta x, thg thi cd
b E A sao cho
x = ab.