Determine all possible triplet(s) (P, Q, N) of positive integers, with P < Q and N ≥ 3, such that the decimal representations of P^N and Q^N will together contain each of the digits 0 to 9 exactly once. Neither P^N nor Q^N can contain any leading zero.

I used the following Mathematica code to find the only solution of

(21,93,3) which gives 21^3=9261 and 93^3=804357

For[q=2,q„T995,q++,

For[p=1,p<q,p++,

n=3;

v1=p^n;

v2=q^n;

dgts=Sort[Flatten[Append[IntegerDigits[v1],IntegerDigits[v2]]]];

While[Length[dgts]„T10,

If[dgtsƒú{0,1,2,3,4,5,6,7,8,9},

Print["(",p,",",q,",",n,") ",v1," ",v2];

];

n++;

v1=v1*p;

v2=v2*q;

dgts=Sort[Flatten[Append[IntegerDigits[v1],IntegerDigits[v2]]]];

];];];

Posted by Daniel on 2009-05-12 13:10:34