When dealing with negative numbers recall:
if A is a negative number: A = Q * B + R
Q = floor(A/B)
For example:
-6 mod 18
Q= -1…floor(-6/18)
A QB + R
-6 = -1 18 + R
12 = R
-6 mod 18 = 12
Solution: -27 mod 4
Q = floor(-27/4) = floor(-6.75) = -7
A = Q B + R
-27 = -7 4 + R
1 = R
Solution: -7 mod 6
A = Q * B + R
-7 = floor(-7/6) + R
-7 = -12 + R
5 = R
Solution: -17 mod 7
A = Q B + R
-17 = floor(-17/7)7 + R
-17 = -3*7 + R
4 = R
