Page 49 - Numbertheory

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.  2000 = 95 .x 2000
 21 
21
. 95 − 23 = 72 500 < n < 2000

1323 ( ) : 13 101 ()
1319 ( ) 1317 ( ) 1313 ( )

:( )

101 = 7 ×13 +10

13 = 1×10 + 3

10 = 3× 3 +1

3 = 1.3 + 0

. lcm (101, 13) = 101×13 = 1313 . gcd(101, 13) = 1

1

gcd(a, b ) = 1 ()

a −b a +b

7 2() 3 2( ) 2 1( ) 3 1()

. gcd(a +b , a −b ) = d :( )

d  (a + b + a −b ) . d  (a −b ) d  (a + b )

. d  2b d  2a .d  (a + b − a + b )

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