Modular arithmetic is something we become familiar with at a very early age. We use it as soon as we learn to tell the time. On a standard clock, we count hours modulo 12, which means that as soon as we reach 12 we start again at 1. (A more sophisticated way of describing this is to say that in mod 12 arithmetic the numbers 12 and 0 coincide.) On a 24 hour clock, hours are counted modulo 24. On either clock, minutes are counted modulo 60, as are seconds. Days of the week are counted modulo 7, months modulo 12.
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