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If it is Monday today, what day of the week will it be 23 days from now? What about 49 days from now? If you stopped to answer these questions, you probably did it without having to count out 23 or 49 days. Both have to do with division and remainders. Since every seven days, the day of the week repeats, to figure out the day of the week, we just need to know how many extra days over a full week there are. In other words, if we are interested in what day of the week it is some number of days from now, we only need to know the remainder when that number of days is divided by seven—it doesn’t matter how many full weeks have gone by. When 23 is divided by 7, the remainder is 2 because 23 = 3(7) + 2. So, if today is Monday, it will be Wednesday in 23 days. And, since dividing 49 by 7 leaves a remainder of 0 (because 49 = 7(7) + 0), it will be Monday again in 49 days. This chapter discusses the concepts of congruences and modular arithmetic.
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Agnes M. Rash
- Chapter 6
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