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A repunit is a number consisting only of the digit 1, such as 111 and 11111. Find the number of digits in the smallest repunit divisible by 21 and 9.

 Jul 18, 2022
 #1
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+1

LCM [9, 21] ==63

 

[10^63  - 1] / 9  mod 9 ==0

[10^63  - 1] / 9 mod 21 ==0

 

So, 63 reunits is the smallest number that will divide 9 and 21

 Jul 18, 2022
 #2
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+1

111,111,111,111,111,111 / 9  =  12345679012345679 × 9 + 0 

111,111,111,111,111,111/ 21  = 5291005291005291 × 21 + 0

 

 

 

 

cool cool cool

 Jul 18, 2022

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