P.~Erd\H{o}s \& Richard K.~Guy, Distinct distances between lattice points, {\it Elem.\ Math.} {\bf 25}(1970) 121--123; {\it MR} {\bf 43} \#7406; {\it Zbl} {\bf 222}.10053; {\it RZh} 1971 5A153. --Oh. This article by Erdos+Guy did the same stuff I did in my math-fun post only they did it 45 years earlier. Except for my conjectured lower bound N^(1-o(1)). My suggested method for proving that conjecture depends on methods which I believe did not yet exist in 1970, and actually may not even quite exist now. But I think it may well be possible to prove it with more work, perhaps via a variant of the Rodl "nibble" and/or Spencer "randomized greedy" techniques I mentioned to handle the missing final stage of the argument. Recommend investigating. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)