Page 73 - Numbertheory

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14414 = 7207
14 7

14416 = 7208
14 7

14418 = 7209
14 7

7 7208 47 7207
7209
.6 7 5

14 14414×14416×14418

. 8 14 4×5× 6

n [Aust.MC 2003] ( )

9( ) 63 10n −1

8( ) 6( ) 5 ()

10n −1 = 999...9 63 = 7 × 9 :( )
.9
7 .7
10n −1 n
.7
105 −1 = 99999

106 −1 = 999999 = 7×142857

.n =6

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