# Gaussian Formulae

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The Gaussian Formulae for Pascha were created by the prolific German mathematician Karl Friedrich Gauss (1777-1855).

In these formulae, mod indicates the Modulus, a mathematical operator that returns the remainder from division. For example, [itex]8 mod 3 = 2[/itex] because [itex]8 / 3 = 2 remainder 2[/itex].

In addition, int indicates the Integer Part of a number. For positive numbers, it returns the greatest integer less than the number. For example, [itex]Int(8.25) = 8[/itex].

Year indicates the year of interest (AD).

The formulae:

```a = Year mod 4b = Year mod 7c = Year mod 19d = (19c + 15) mod 30e = (2a + 4b - d + 34) mod 7f = Int((d + e + 114) / 31)g = ((d + e + 114) mod 31) + 1f is the month of Pascha.g is the day of Pascha. For example, if f is 3 and g is 27, then Pascha occurs on March 27.
```

Important, this returns the date of Pascha ONLY on the Old Calendar. To get the Gregorian date, add 13 days during the twentieth and twenty-first centuries.