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Mathematical problems about leap years
The general rules for judging leap years in Gregorian calendar are: leap every four years, not leap in a hundred years, and leap again in four hundred years.

Accurate calculation method of leap year in Gregorian calendar: (according to a tropical year, 365 days, 5 hours, 48 minutes and 45.5 seconds)

(1) leap year refers to a year in which ordinary years are divisible by 4, but not by 100. (For example, 2004 is a leap year, 1900 is not. )

② Leap year is a year that can be divided by 400 but not by 3200. (For example, 2000 is a leap year, but 3200 is not)

(3) A year with a large number can be divisible by 3200, but it can also be divisible by 172800, which is a leap year (for example, 172800 is a leap year, but 86400 is not).

According to: (calculated according to the tropical year of 365 days, 5 hours, 48 minutes and 46 seconds), the rules of leap year in BC are as follows:

(1) leap year refers to a year in which ordinary years are divisible by 4, but not by 100. (For example, 2004 is a leap year, 1900 is not. )

② Leap year is a year that can be divided by 400 but not by 3200. (For example, 2000 is a leap year, but 3200 is not)

(3) A year with a large number can be divisible by 3200, but it can also be divisible by 86400, which is a leap year (for example, 86400 is a leap year).

Reason: A year is calculated as 365 days, 5h48'46'', and the number of days in a year must be an integer, so it is not convenient to count the hours. So take 365 days as a year, and the remaining 5: 48 minutes and 46 seconds, four years will accumulate to about one day, so a leap day in four years is called a leap year, and a year without leap days is a normal year, that is. But by four years, it was only 23: 15 minutes and 4 seconds, missing 44 minutes and 56 seconds; When the product arrives at 100 (25 leap years), it is still short of 18: 43: 20 seconds, about 3/4 days, so it will not leap at 100; At this time, it is 5: 16: 40, and it has accumulated to 400 years, 2 1: 6: 40, leap; We are still short of 2: 53: 20. If we accumulate to 3200, we will be short of 23: 6: 40. After 3200, it will not be a leap. At this time, there are 53 minutes and 20 seconds left, and the product is just another leap at 24 o'clock in 86400. This is neither a surplus nor a deficit and needs to be recalculated, so the leap year rule above is calculated according to the solar calendar.

According to the tropical year of 365 days, 5h48'45.5'', 3200 is 16000 hours, 153600 minutes, 145600 seconds = 18600 hours, 26 minutes and 40 seconds, * * 18600 hours, so it can only be counted as 775 leap years, and 3200 is not a leap year, so 775*24= 18600, how many cycles will it take to make up the extra 26 minutes and 40 seconds? The answer is 54 cycles, that is, 172800, because 172800/3200=54 cycles 54*26 minutes 40 seconds = 1404 minutes 2 160 seconds =24 hours.

The rules for leap years in BC are as follows:

1, not a whole hundred years: the number of years is divided by 4, and the remainder 1 is a leap year, that is, 1, 5,9 ... BC;

2. Whole hundred years: the years divided by 400 are 1, the years divided by 3200 are 1, not leap years, and the years divided by 172800 are 1, that is, 40 1 and 80 1 BC.