N is a positive integer. When N is divided by 3, the remainder is 2. When N is divided by 4, the remainder is 1. What is the remainder when N is divided by 12?
N mod 3 = 2 ⇒ 3a + 2 = N
N mod 4 = 1 ⇒ 4b + 1 = N
3a - 4b + 1 = 0
3a = 4b - 1
a b
5 4
9 7 ......
3(5) + 2 = 17
4(4) + 1 = 17
3(9) + 2 = 29
4(7) + 1 = 29
17 mod 12 = 5
29 mod 12 = 5 ......etc
