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String of 3s (Posted on 2025-05-16) Difficulty: 3 of 5
A number written as a string of 32013 digit 3s. No other digit appears. Find the highest power of 3 which divides this number.

No Solution Yet Submitted by Danish Ahmed Khan    
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re(2): curious | Comment 3 of 6 |
(In reply to re: curious by Charlie)

My confusion is probably the result of the temptation to think that  the number is 3 times a repunit of length 2013, but it's actually of length 3^2013. If it had been the former, the number itself would still be a multiple of 9 as the digits of 2013 are a multiple of 3, and there's the multiplication of that by 3.


But as the repunit is of length 3^2013 it is certainly itself a multiple of 9 and possibly of higher powers of 3, assuring that the number in question is least a multiple of 27, but it could be a higher power of 3 than that.

  Posted by Charlie on 2025-05-17 06:05:47
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