[gfodor]

Meh, this is cool and all but is just a coincidence of base-10 notation, not some fundamental theorem about the integers.

[msds]

In fact, searching for x such that 1+4x10^(Ceiling[Log10[x]])-4x^2 is a perfect square gives you tons of integers that make up half of a pair that has this property. 123288,328768 is my favorite pair, for arbitrary reasons.