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


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.




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