Page 78 - Numbertheory

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x 12 x [Aust.MC 2001]( )

7 x2 9

100 60 ( ) x
200 150 ( )
60 50 ( )
150 100 ( )

12 9 x −2 : ( )

. 36 .
.182 . 2 36
x
5
. 38, 74, 100, 146, 182, 218, ... x

7 .( )
n [Aust.MC 1997] ( )

12 4 7 ()
()
42 32 ( ) :
72 60 ( )
31 19

58 51

:( )

n = 12k + 5 = 7k + 5(k +1)

. 7 5(k +1) 7 n
4
5(k +1) k

. n = 12× 4 + 5 = 53 .k =4 7

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