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It is not 8^5 (Posted on 2015-06-24) Difficulty: 2 of 5
In decimal representation find the largest N-digit number which is an N-th power.

See The Solution Submitted by Ady TZIDON    
Rating: 5.0000 (1 votes)

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Solution re: Solution (Spoiler) | Comment 2 of 3 |
(In reply to Solution (Spoiler) by broll)

I interpreted the puzzle differently from broll. I thought the request was to find the generalized answer for various N, such as 81 is the largest 2-digit number that's a perfect square (16, 25, 36, 49, 64 being others); 729 is the largest 3-digit cube (125, 216, etc. being others), etc. So I thought:

9^N will work up through N=21. Beyond that there does not exist an N-digit number that's a perfect Nth power.

9^21 is the 21-digit number 109418989131512359209, while 9^22 is also a 21-digit number: 984770902183611232881. It's all downhill from there.

  Posted by Charlie on 2015-06-24 09:48:19
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