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Pandigital powers (Posted on 2021-04-07) Difficulty: 2 of 5
What positive integer n has the property that n2 and n3 together contain every digit from 0 to 9 exactly once?

No Solution Yet Submitted by Math Man    
Rating: 5.0000 (1 votes)

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Some Thoughts re(2): Analytic attempt...? | Comment 4 of 5 |
(In reply to re: Analytic attempt...? by Steve Herman)

Great catch, can't believe I didn't think of checking mod 9 after checking mod 3.  That's what I get for solving before coffee in the morning.  

I think n could be 8 mod 9 though, since n^2 would be 1 mod 9 and n^3 would be 8 mod 9, so the sum of all their digits would also be 0 mod 9.  

Edited on April 7, 2021, 2:28 pm
  Posted by tomarken on 2021-04-07 14:28:14

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