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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: Analytic attempt...? | Comment 3 of 5 |
(In reply to Analytic attempt...? by tomarken)

The sum of all digits from 0 through 9 is 0 mod 9, so n cannot be 1,2,4,5,7,8 mod 3, since n^2 + n^3 would not be 0 mod 9.   n must therefore be divisible by 3.  That gets tomarken's list down to 


54
63
69
72
84
87

It also eliminates the need for some of the "brute forcish" methods he used to eliminate 89, 94, 97, 98, 68, and 92. 

  Posted by Steve Herman on 2021-04-07 10:59:20
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