Page 82 - Numbertheory

@ @Hßìÿa@ö§aI@†a‡Èÿa@óî‹Åä@@

gcd(2002 + 2, 20022 + 2, 20023 + 2) [HMMT 2002]( )

6() 4( ) 3( ) 2 ()

: ()

n 3 n3 −n ( )

n 4 n4 −n ( )

n 6 n6 −n ( )

n 8 n8 −n ( )

: n 5 − 5n 3 + 4n n ()

120 ( ) 93( ) 81( ) 79 ( )

31986 − 21986 [Mathcounts 1986] ( )

9( ) 7( ) 5( ) 4 ()

1 5n [Mathcounts 1991] ( )

5 3n

4( ) 3( ) 2( ) 1 ()
30 ( )
n = 11111111112 [Mathcounts 1986] ( )

20 ( ) 14 ( ) (3n )2 )

8 [AHSME 12 ( )
1954] (

6432 132

8( ) 6( ) 4( ) 2 ()

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