Question 129894
Find an integer having remainders of 1, 2, 5, 5, when divided by 2, 3, 6, 12 respectively.
Well, intuitively, you can see that the required integer has to be equal to or larger than 12+5, right?
In fact, you can go farther and say that it can be equal to n*12+5, where n is any non-zero positive integer (1, 2, 3, ...).
Let's try some:
n = 1, so n*12+5 = 17
17/2 = 8 & R=1
17/3 = 5 & R=2
17/6 = 2 & R=5
17/12 = 1 & R=5
So 17 is such an integer and it happens to be the smallest such integer.
Here are some others that you can try:
2*12+5 = 29
3*12+5 = 41
4*12+5 = 53
5*12+5 = 65,...