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. .12 3 x() )
x () )
n . n3
6( ) n [AMC12B 2010] (
5( )
n n2 20
53
53 7( ) 8 ()
(
n
. 12
n + 60 ( ) n +12 ( ) n+5 ( ) 12
n+3 () )
n(
gcd(n, 2n +1) = 1 gcd(2n, 3n ) = n ( )
gcd(n, 2n +1) = n gcd(2n, 3n) = 1 ( )
gcd(2n,3n) = gcd(n, 2n +1) = 1 ( )
gcd(2n, 3n) = gcd(n, 2n +1) = n ( )
. S = 1!+ 2!+ 3!+ ... + 99! [AHSME 1978] ( )
S
3() 5( ) 8( ) 9 ()
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