November 22, 2021, is a Monday. But what day of the week will Christmas fall on in 2021?
And in 2022? Clearly, the remainders when 30, 31, or 365 are divided by 7 play a fundamental role in answering these questions. We will not insult you by spelling out the calculation.
What emerges, however, is that working with remainders is just as effective for everyday problems as it is for deep results in number theory.
Quotient sets and congruences
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To study certain properties of integers, it is sometimes enough to consider only their remainders upon division by a given integer n. What if, instead of considering the infinite set of integers, we settled for the set of their n possible remainders? No sooner said than done: thus was born the set /n, a set of n elements known as a quotient set, which makes certain results considerably easier to obtain.
