Of course replace "magic sum" by "magic product", twice in my previous message... -----Message d'origine----- De : math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com [mailto:math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com] De la part de Christian Boyer Envoyé : jeudi 22 septembre 2005 16:30 À : 'math-fun' Objet : RE: [math-fun] Multiplicative Magic Squares In his old book on recreative mathematics, Boris Kordiemski described exactly the Michael's method (using two latin squares) for 4x4 multiplicative squares. He also described a method for 3x3 multiplicative squares: a b² a²b a²b² ab 1 b a² ab² With a=2 and b=3, you get 2 9 12 36 6 1 3 4 18 Magic sum = 216 (*). It is the smallest possible multiplicative square. In 1667 (a long time ago...), Arnauld gave a 3x3 multiplicative square. Perhaps the oldest published multiplicative square? Using powers of 2, its magic sum was bigger : 4096. Christian. (*) 216 is also the smallest cube being also sum of three cubes. 216 = 6^3 = 3^3 + 4^3 + 5^3 _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun