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.