Next to the day, the week is the most significant block of time in modern life. A week i...

Next to the day, the week is the most significant block of time in modern life. A week is a cycle of seven days. Determining the day of the week at some point in the future is a modular arithmetic problem. For example, because mod 7, we know that if January 4 is a Monday, then January 11 will also be a Monday.

a. If today is Monday, use congruence modulo 7 to determine what day of the week it will be in 61 days.

b. If March 1, 2004 was a Monday, use congruence modulo 7 to determine the day of the week on which January 15, 2006 fell.