Nice argument. Can we satisfy a+b+c = abc two different ways as a first step towards a 4x4? ----- Original Message ----- From: "Michael Kleber" <michael.kleber@gmail.com> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Friday, September 23, 2005 10:02 AM Subject: Re: [math-fun] Multiplicative Magic Squares David Wilson wrote:
Can a 3x3 magic square be both additively and multiplicatively magic?
Not even close, even if you don't try for diagonals. There's at most one solution to {x+y=S, xy=P} for any S and P -- as we were taught when we learned to factor polynomials -- and any z in a both-ways-magic square would force its row-mates and column-mates to be two solutions to such a system. Nice work on the possible 4x4 magic products, by the way... --Michael Kleber -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun