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??? ? ?? ?? a, b ? ???

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Title: PowerPoint Author: pc34142 Last modified by: HJC Created Date: 9/24/2002 3:00:21 AM Document presentation format: – PowerPoint PPT presentation

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Title: ??? ? ?? ?? a, b ? ???


1
???? ???? ???
? ? ? ??? ? ? ? ??? 4?? ???
2
???? ????? ? ??? ? ?? ?? a, b ? ??? a, b ?
?????? ?? ??? ???. ?????? ?? ?? ? ?? ??? ?? ???
???? ? ???? ?????? ????? ???? ???? ???? ?? ???
? ??.
3
???? ???? ??? ??? ???? ? ?? ?? ? ? ?? ?? ?? ????
?? ???? ??? ??. ?? ?? a ? b ? ????? ?? q ??
???? r ? ???? a bq r ? ?? ????. ? ?, a ? b ?
?????? b ? r ? ?? ???? ?? (r? 0? ??? a ? b ?
?????? b? ??) ?? ?? ???? ???? ????.
??? ?? ?? ??? ??? ?? ????? ??...
4
EX) (33, 18)? ???? ???. 33, 18 ? ?????? d ?? ??,
33 181 15 ??? 18, 15 ? ?????? d ??. 18
151 3 ??? 15, 3 ? ?????? d ??. 15, 3 ?
?????? 3 ???, d 3 ?? ?? ? ? ??.
? ??? ??? ?? ???? ???? ????
33 18
33? 18? ???.(?1,???15) 18? 15? ???.(?1, ???3) 15?
3?? ???.(??? ???) ??? ???? ??(??? ?)? ????? ?,
(33, 18)3
1
1
18
15
15
3
5
15
0
5
???? ???? ?????.
a qb r ( a,b,q,r? ??? ??) a ? b ? ?????? b ?
r ? ?? ???? ?? (??) ??? gcd(a,b)gcd(a-qb,b) ??
??? ????. gcd(a,b)d , gcd(a-qb,b)s ?? ??
1) d s ?? ?????. d I a d I b d l qb gt
d I a-qb ??? d? b? a-qb? ??? S? a-qb? b?
???????? ds?? ? ? ??.
6
2) d s ?? ????? s I a-qb s I b
s I qb gt s I (a-qb)qba ??? s? a? b?
?????. d? a? b? ???????? d s ?? ?
? ??. 1), 2)? ??? d s , d s ???
ds
7
???? ??? gcd(a,b)gcd(a-qb,b)? ???? gcd(2424869,95
09)? ?????? ??..
gcd( 2424869, 9509) gcd( 2424869-255 9509,
9509) gcd ( 74, 9509) gcd (74 ,
9509-12874 ) gcd (74, 37) gcd (74-237,
37) gcd(0 , 37) 37 ??? gcd(2424869,9509)37
?? ?? ? ??.
8
?? ???? ??? ? ??
2424869 9509
200
100
-1901800
-7400
50
523069
2109
20
-475450
-1480
5
47619
629
8
-47545
-592
74
2
37
?? ???
-74
0
9
???? www.banyo.ms.kr/no1122/number/uclid.htm lt???
???gt, ???, ???
?? ? ???? ?? ? ?? ??? ??? ???? lt??gt? ?????.
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