Page 77 - Numbertheory

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RQ P 9 S ≤ 12

.S =9 .9

1+1+1 + 1 n( ) n [AMC10B 2002] ( )
237n n > 34 ( ) .

3 2 n ()
n < 21( )

0 < 41 + 1 < 41 + 1 < 2 1 + 1 + 1 = 41 :( )
42 n 42 1 2 3 7 42

. n = 42 . 41 + 1 =1
42 n

m [Aust.MC 2001] ( )
12 ( ) 10 ( )
24, 42, m

m . 6, 15, m

30 ( ) 15 ( )

. gcd(24, 42) = 6 :( )
. gcd(24, m ) = 6
. lcm (6,15) = 30
. m = 30 . 30 .m 6
m . lcm (6, m ) = 30

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