![]() ![]() ![]() So, for example, when working modulo 7 we find that 37 is congruent to 2, since 35 is a multiple of 7 and 37 – 35 = 2. (This should make intuitive sense: if it’s currently 12 o’clock then in 5 hours it will be 5 o’clock and 7 hours ago it was also 5 o’clock.)įor calendar calculations, we need to work modulo 7 (because there are 7 days of the week) and modulo 4 (because every 4 years there is a leap year). We can also go backwards: for example, by subtracting 12 we see that 5 is congruent to -7. Similarly, when we work modulo 12, 5 is congruent to 17, which is also congruent to 29. ![]() For example, arithmetic modulo 12 is often called clock arithmetic: 13 o’clock is the same as 1 o’clock, so 13 and 1 are congruent modulo 12. When we do arithmetic modulo m, it means that we are allowed to add or subtract multiples of m at will without changing the answer. I’ll present both systems in a way which allows for a direct comparison of their relative merits and let you, dear reader, decide for yourself which one to learn.Ī basic prerequisite for understanding these two algorithms is a rudimentary knowledge of modular arithmetic. I personally use a modified verison of the apocryphal method. In this post, I’ll present two of the most popular systems for doing this, the “Apocryphal Method” and Conway’s Doomsday Method. In this previous post, I recalled a discussion I once had with John Conway about the pros and cons of different systems for mentally calculating the day of the week for any given date.
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