Already three volunteers! It should be sufficient, thanks. Christian. -----Message d'origine----- De : math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] De la part de Christian Boyer Envoyé : jeudi 29 janvier 2009 15:46 À : 'math-fun' Objet : [math-fun] New add-mult squares Help needed! Look at this matrix: 75 38 207 102 11 20 91 56 5 44 49 104 57 50 153 138 133 200 17 92 45 66 21 26 99 30 39 14 175 152 23 68 78 63 22 15 184 119 100 19 136 161 76 25 42 117 10 33 28 13 40 77 34 69 114 225 46 51 150 171 52 7 88 35 If you ADD the numbers of each row or column or diagonal, always the same sum S = 600. If you MULTIPLY the numbers of each row or column or diagonal, always the same product P = 67463283888000. This kind of object is called an additive-multiplicative (or addition-multiplication, or add-mult) magic square. Some few 8x8 and 9x9 squares are known: http://mathworld.wolfram.com/Addition-MultiplicationMagicSquare.html But larger squares (10x10 and above) are extremely rare, most of them being unknown. I have some new squares, from 10x10 to 25x25. But before their publication, I would like to be sure that they are fully correct. If you can help me, checking these squares (and that the n^2 used integers in each nxn square are distinct, very important...), send me a private message. Thanks in advance! Integer values < 15,000 Products P < 10^80 (multiprecision needed) Christian. www.multimagie.com/indexengl.htm _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun