An addition-multiplication square is a square of integers that is simultaneously a magic square and multiplication magic square. In 1955, Horner found a square of order eight with addition magic constant 840 and multiplicative magic constant 2058068231856000, and largest number 261 (left figure; Horner 1955, Hunter and Madachy 1975). In 2005, Boyer found a smaller order-eight square above with addition constant 600, multiplicative constant 67463283888000, and largest number 225. Boyer also found a square with smaller multiplicative constant 51407948592000, but larger addition constant (760) and largest number (333).
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