The Gregorian calendar (the one in most general use today) is the same as the Julian calendar except that there are 365 days in year x if x is congruent to 100, 200, or 300 modulo 400. (a) In the Gregorian calendar, as students of World War II may recall, 7 December 1941 was a Sunday. We cannot, as in the case of the Julian calendar, guarantee that 7 December of year x was a Sunday if x 1941 (mod 28), but we can guarantee it if x 1941 (mod c) for some value of c. Find the smallest value of c for which this is true. (b) Determine the day of the week on which you were born, using only the fact that 7 December 1941 was a Sunday. Show all of your reasoning. (c) What additional complications arise when designing a perpetual Gregorian calendar? (d) In what years, during the period from 1 to 1941 A.D. (or 1 to 1941 C.E.), have the Gregorian and Julian calendars agreed for the entire year?