Enigma 40: Six Squares
30 January 2012
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From New Scientist #1182, 22nd November 1979 [link]
“Since last year”, said Mr Knull, “when I read in M500/52 of a puzzle which its proposer John Hulbert described as a ‘glorious time waster’, I have been struggling with two versions of it. I wonder if you can help me with the easier version? It is quite simple to state. Find three different integers, P, Q and R, such that P+Q, P+R, Q+R, P−Q, P−R, and Q−R are all perfect squares. Any questions?”
“Just one”, I said. “Is 0 an integer? I always forget.”
“Of course it is”, said Mr Knull. “And so of course are −1, −2 and so on”.
What is the smallest such set of three different integers you can find? By smallest I mean with P+Q+R as small as possible.
This puzzle is revisited in Enigma 45.