September begins on the same day of the week as December every year, because there are 91 days separating September and December, which is a multiple of seven (the number of days in the week). No other month ends on the same day of the week as September in any year. This month and May are the only two months to have this property. April and July of the previous year begin on the same day of the week as September of the current year as a common year, October of the previous year always begins on the same day of the week as September of the current year as a leap year, January of the previous year begins on the same day of the week as September of the current year as a leap year and a year immediately before that. In common years, September ends on the same day of the week as April and December of the previous year while in leap years, September ends on the same day of the week as July of the previous year. In years immediately before common years, September begins on the same day of the week as June of the following year and in years immediately before leap years, September begins on the same day of the week as March and November of the following year. In years immediately before common years, September ends on the same day of the week as March and June of the following year and in years immediately before leap years, September ends on the same day of the week as August and November of the following year.
https://en.wikipedia.org/wiki/September
