Page 86 - Numbertheory

@ @Hßìÿa@ö§aI@†a‡Èÿa@óî‹Åä@@

P (n) S (n) [AMC10 2001] ( )
)
N. n )

N N = P (N ) + S (N ) )
)
3( ) 6( ) 8( ) 9 ()

9 b ×105 + c ×103 b +c = 9 (

3( ) 2( ) 1( ) 0 ()

(

n2 −1 n = 4k +1 ()

.8

.n n2 + n +1 n3 −1 ( )

n +1 nm + n + m +1 ( )

.m n

.n 3 n2 −2 ( )
42 ( )
n [AMC10 2001] (

.7 n
.
28 ( ) n 6 ()

21 ( )

. 2x − x [AMC12A 2008] (

36

. x ()
.3 x ( )

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