Introduction To Modular Arithmetic

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Introduction To Modular ArithmeticFebruary 22, 2015Olga RadkoOleg Up ProblemIt takes a grandfather s clock30seconds to chime6o clock. Assuming that the time of eachchime is negligible compared to the time intervals between the chimes, how much time wouldit take the clock to chime12?Clock Arithmetic or a Circle as a Number LineOne way to turn a circle into a number line is to divide it into twelve equal parts. In this case,one step is usually called one 2It takes a grandfather s clock 30 seconds to chime6 o clock. How much time would it take the clock to chime 12?Clock Arithmetic or a Circle as a Number LineOne way to turn a circle into a number line is to divide itinto twelve equal parts. In this case, one step is usually calledone coincides with 12. The hour hand moves from 0 to 1, from1to2.

15 14 13 12 23 22 21 20 19 18 17 16 0 coincides with 12. The hour hand moves from 0 to 1, from ... Moreover, we can define operations of addition and multiplication in the modular arithmetic: ... table you made problem 10(c), we see that c ⌘ 6 (mod 7). Thus, we write 3÷4 ⌘ 6 (mod 7) This is true because 6⇥4 ⌘ 3 (mod 7).

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