Burt Kaliski Jr. (@modulomathy)

4/1/12 10:35 PM

#math trivia for #April1: #92 = 7*13+1, so April is congruent to January; both start on Sunday. What other months are congruent this year?

The answer is a simple matter of modular arithmetic. Reduced modulo 7, the lengths of the 12 months in a leap year follow the sequence

3 1 3 2 3 2 3 3 2 3 2 3

The starting days of the month thus have the modular values (relative to January 1)

0 3 4 0 2 5 0 3 6 1 4 6

The congruent months this year are

— January, April and July

— February and August

— March and November

— September and December

January 13 was a Friday. Due to the congruences, there was also be a Friday the 13th this year in April, and a third one, the maximum for any year, in July.

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