2: A non-leap year consists of 365 days. If we evaluate 365 in mod 7, we see that 365 ≡ 1 (mod 7).
a = 365 and n = 7
365 ≡ b (mod 7)
365 - b = 7n
n = 52, since (52)7 = 364
then b = 1, since 365 - 1 = 364
52 cycles of 7, or 52 weeks, exist in each non-leap year with one extra day.
Because b = 1, each January will begin on the next consecutive day of the week.
A leap year consists of 366 days, so b = 2. Therefore, the January after a leap year will begin on the second day of the week after the previous year.
Let 1998, which is a non-leap year, be represented by x. January 1st will fall on Thursday again and both February and March will have a Friday 13th in 11 years. Although January 1, 2004 falls on a Thursday, it is also a leap year. Therefore, only February will contain Friday 13th.