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.

(In reply to computer solution by Daniel)

I see Daniel has expanded the range I used, and shows no other solutions possible.  I do not know how Mathematica works, and I see an assignment n=3, but then also "n++" which I assume tests higher exponents in the same (p,q) loops, until values exceed ten digits (the "T10"?). I also tried n=4 and 5, and found quite a few pandigital(1..9) but none (0..9).  That is a powerful package, but what a syntax!  Nice proof!

 

Posted by ed bottemiller on 2009-05-12 14:27:12