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Digits of N^3 (Posted on 2024-04-25) Difficulty: 3 of 5
Determine a positive integer N such that the digits of N combined with the digits of N^2 are exactly the digits of N^3.

Extra credit: Find additional solutions, other than multiples of 10.

  Submitted by K Sengupta    
Rating: 5.0000 (1 votes)
Solution: (Hide)
N values up to 10^8 with my definition of "exact" and no trailing zeros:
[6894, 579492, 730971, 2292309, 
2906289, 5324499, 5920119, 
7292088, 7893621, 7934391, 
8250237, 8494146, 9419976, 
22716252, 23488173, 24272199, 
24426189, 24933087, 27130293, 
27575037, 28274238,30828231, 
31052907, 48755196, 52094736, 
52235892, 53376966,53547345, 
54022374, 54542646, 57842469, 
60228279,61306623, 66317535, 
71397864,71465994, 72034776, 
74244906,74695122, 75395682, 
76813065,77984271, 82153485, 
82500435,82506717, 84380958,
87264504,87907491, 89179353, 
89233416, 90815346, 93047805, 
93138201,93215655, 93641004, 94235976,
94361211,98219016, 98474931,98869932]
For an explanation, refer to the solution submitted by Larry in this location.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some ThoughtsSome solutionsLarry2024-04-25 11:18:56
Solutioncomputer solutionCharlie2024-04-25 09:09:26
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