# Chapter 4 - Elementary Number Theory and Methods of Proof - Exercise Set 4.4 - Page 189: 13

Wednesday

#### Work Step by Step

The formula for the day of the week in $N$ days is $DayN = ((DayT)+N)\ mod\ 7$, where $DayN$ is the day of the week in $N$ days, $DayT$ is the day of the week today, and the days Sunday through Saturday are numbered $0$ through $6$, respectively. Therefore, if $DayT=1$ and $N=30$, we have $DayN = (1+30)\ mod\ 7=31\ mod\ 7=3$, because $31=7(4)+3$. See example 4.4.3 for an explanation of the formula $DayN = ((DayT)+N)\ mod\ 7$.

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