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For example, September and December correspond, because 1 September falls on the same day as 1 December (as there are precisely thirteen 7-day weeks between the two dates). Months can only correspond if the number of days between their first days is divisible by 7, or in other words, if their first days are a whole number of weeks apart.
The doomsday's anchor day calculation is effectively calculating the number of days between any given date in the base year and the same date in the current year, then taking the remainder modulo 7. When both dates come after the leap day (if any), the difference is just 365 y + y / 4 (rounded down).
In the second line, the number one is added to the fraction, and again Excel displays only 15 figures. In the third line, one is subtracted from the sum using Excel. Because the sum has only eleven 1s after the decimal, the true difference when ‘1’ is subtracted is three 0s followed by a string of eleven 1s.
In the figure, the fraction 1/9000 is displayed in Excel. Although this number has a decimal representation that is an infinite string of ones, Excel displays only the leading 15 figures. In the second line, the number one is added to the fraction, and again Excel displays only 15 figures. In the third line, one is subtracted from the sum using ...
For example, if the fiscal year end month is August, the company's year end could fall on any date from August 25 to August 31. In particular, the last fiscal week is the one that includes August 25 and the first fiscal week of the following year is the one that includes September 1. In this scenario, fiscal years would end on the following days:
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Zeller's congruence is an algorithm devised by Christian Zeller in the 19th century to calculate the day of the week for any Julian or Gregorian calendar date. It can be considered to be based on the conversion between Julian day and the calendar date.
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