Page 81 - Numbertheory

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29 ( ) 27 ( ) gcd(1769, 2378) ()
12n +1 ( ) ()
25 ( ) 23 ( )
6445( )
n
1( )
a+2 ( ) 30n + 2 12n +1

6n +1( ) 3( ) 1 ()

lcm (117, 165) ()
()
6440 ( ) 6435 ( ) 6430 ( )
()
: c |(a +b ) gcd(a, b ) = 1 ()

. gcd(a, c ) ≠ gcd(b , c ) ( )

gcd(a, c ) = 2 gcd(b , c ) = 1( )

gcd(b , c ) = 1 gcd(a, c ) = 1( )

gcd(b, c ) = gcd(a, c ) = 1 ( )

(n +1)!+1 n!+1

(n +1)! ( ) n!+1( ) n!( )

lcm (a, a + 2) a

a ( ) 1a(a + 2) ( ) a(a + 2) ( )

2

٦٨