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The power of 37 (Posted on 2021-06-17) Difficulty: 3 of 5
What is the greatest value of n such that the number 11...11 (the 3*372000 digit repunit) is divisible by 37n?

No Solution Yet Submitted by Danish Ahmed Khan    
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re(2): Puzzle Answer Comment 5 of 5 |
(In reply to re: Puzzle Answer by Wendy Morgan)

That's a fascinating problem! Breaking down large repunits into divisible chunks is always tricky. It seems like finding the prime factorization of 37 and then working to see how many times those prime factors appear in the repunit's factorization is the key. I wonder if anyone's tackled this using modular arithmetic? Also, this makes me think about other games, like that addictive little game Monkey Mart, where efficient resource management and scaling up are crucial for success. Just like in that game, understanding the underlying structure helps optimize everything. I'm curious to see what solutions others come up with for this repunit problem! It's definitely a brain teaser.

  Posted by hannahzemlak on 2025-04-28 21:07:01

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