Transcription of Magic Squares and Modular Arithmetic - Math
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Magic Squares and Modular Arithmetic - Math
Magic Squares and Modular ArithmeticJim CarlsonNovember 7, 20011 IntroductionRecall that amagic squareis a square array of consecutive distinct numberssuch that all row and column sums and are the same. Here is an example, amagic square oforderthree:8 1 63 5 74 9 2 Fig. 1 The common row (or column) sum is called themagic sum. In Figure 1 above,the Magic sum is 15. This is the first known example of a Magic square , takenfromLoh-Shuscroll in China. Some scholars date it to the mythical founder ofChinese civilization,Fuh-Shi, 2858-2736 BC.
Introductory problems 1. Find a magic square of order three whose first row is 0 8 4 2. Find a magic square of order three whose first row is 1 8 3
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