A
^{5} + B
^{5} + C
^{5} + D
^{5} + E
^{5} = ABCDE
where each separate letter represents a different digit and A is not zero.
What is ABCDE?
Take
A > B > C > D > E
and suppose that each of A,B,C,D,E have the same sign. (We can take this as positive, since A,B,C,D,E would be equally a valid solution).
then A<sup>5</sup> > ABCDE so that the left side is greater than the right side. This is impossible, so that some of the elements must be negative.
More to come if I have time & ideas.

Posted by FrankM
on 20090503 19:17:23 