Page 229 - Math Grade 12 (Advance)

PROEUS DARA
1.6. t9~tntU~ ( Bezout) 8~t9~tr9it[Hu (Gauss)

fi.· u9rutr9Uril {Etienne Bezout (1730-1783) nn!lnl9mn~ )
n u u

au+ bv = I '1

ML'Eflt!JffllJUf :

e ttl a stl b dlUSStH~l§n'ltlffl tS'H GCD(a, b) = 1 '1
u ct
n:mfimm HitlfitlHUl§tS a stl b dlnttHUl§tS ax, by Stl z = ax+ by ftHli
"l.Ju u u u
x stJ y mussf.i~Gl§mti '1
,. u ...

0 I c:j; QJ ~ cJ
1:1tHSg 'i:!lSuSSf.ifiHiln!f'U u Stl v &1:1ru ua+vb = 1 '1
U U I \.J.
c:;l QJ 0 I Q ef
"fuHul§n~mC'U'i:!lSuSSf.ifi u Stl v t1:1ru ua+vb = 1
l.j " u

1:1msg d dlntun'fs ua+vb tfi ua+vb =I '1
u u
~msg d dl~funtS 1 sl2J a Stl b

1:1msg a stl b dlussm~l§~tltlm '1
u u ct
" . "
n.Jtmfi~! 1: ~n GCD(l2, 18) Stl GCD(l2, 18 x 5) Wn5S~S GCD(12, 18) Stl
u
.. c;t
GCD(l2, 18x5) '1

tf.i(f!S GCD(l2, 18) = 6 Stl GCD(l2, 18x5) = GCD(l2, 90) = 6

1:1msg tf.iffiutuS~S(f!SGl GCD(l2, 18) = GCD(l2, 18 x 5) '1
u .. c;t
Wtmtrttt2: 'Utllmm c stl a 'UUl§~tltlffl rug~ff1tfi GCD(a, b) = GCD(a, be) '1
II U1"'-' ct lli

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