Page 54 - Numbertheory

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358 = 2 ×179 . d  895 d  358
.d = 179
895 = 5×179
1059 = 5×179 +164
. r = 164
.d − r = 179 −164 = 15

2x + 3y yx ()

17 17

9x + 5y ( ) 2x + 5y ( )
3x + 2y ( ) 9x + y ( )

:( )

9x + 5y = 17x +17y − 4(2x + 3y )

.17  (9x + 5y ) 17  (2x + 3y ) 17  (17x +17y )

n [AIME 1986] ( )

890 ( ) n +10 n 3 +100

900 ( ) 880 ( ) 870 ( )

:( )

n 3 +100 = (n +10)(n 2 −10n +100) − 900

. (n +10)  900 (n +10)  (n 3 +100)

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