Abstract
In this paper, we construct four 3 × 3 magic rectangles whose magic sums and the products of 9 entries equal respectively, and whose 36 entries are distinct positive integers, and using these four magic rectangles construct four addition-multiplication magic squares of order 9, whose magic sums and magic products are equal respectively, and whose entries are 324 distinct positive integers. This implies that there exists an addition-multiplication magic square of order 18.
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