23 Sep
2005
23 Sep
'05
8:02 a.m.
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.