For many years, the Roman Catholic church used the Julian calendar, which has a leap year every year that is divisible by four, making the average calendar year longer than the sidereal year and causing the date of the first day of spring to change gradually.

To correct this, Pope Gregory decreed that Thursday, October 4, 1582, would be followed by Friday, October 15. He also declared that years divisible by 100 would be leap years only if divisible by 400.

For any year since 1582, if one printed two 12-month calendars, one Julian and the other Gregorian, with dates for the days of the month, at least some of the dates would not fall on the same day of the week.

What is the first year for which each day of each month will fall on the same day of the week for both calendars?

Although matching to the degree of approximation with the Gregorian year, the goal is to match the tropical year rather than the sidereal year, that is, with respect to the sun's equinoxes and solstices, rather than which stars are rising and setting at given times of day.

Posted by Charlie on 2025-01-14 09:20:31