Just looking and hoping my finger arithmetic is correct. In the 55440 square, I think you can turn 11s into 3s and the 7s into 5s giving 2^4*3^3*5^2=10800. -----Original Message----- From: math-fun-bounces+mdtorge=sandia.gov@mailman.xmission.com [mailto:math-fun-bounces+mdtorge=sandia.gov@mailman.xmission.com] On Behalf Of ed pegg Sent: Wednesday, September 21, 2005 3:50 PM To: math-fun Subject: RE: [math-fun] Multiplicative Magic Squares If you just use powers of 2, the minimal square with distinct entries has multiplicative constant 1073741824 (2^30). 55440 is much smaller. Is it the smallest? --Ed Pegg Jr --- "Torgerson, Mark D" <mdtorge@sandia.gov> wrote:

Replacement goes a long way. You may take all the 3s in the square below and turn them into 29s. Or some other square having large primes

may be replaced with a square with smaller corresponding primes. Even primes within a particular square may be switched. 55440=2^4*3^2*5*7*11 so you can make a corresponding square with 2*3^2*5*7*11^4. No matter the starting square, this reduction leads to

some sort of minimal representation, where the factorization of the product gives 2 with the largest exponent, 3 the next and so on.

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