Question 176318
The modulo (x mod y) function provides the remainder when one integer (x) is divided by another (y).  So if d does not divide a, then a mod d is non-zero.  Also, if d does not divide b, then b mod d is non-zero.  However, it is possible that (a mod d) + (b mod d) = kd where k is a non-zero positive integer.  


Further (a + b) mod d = (a mod d) + (b mod d) so (a + b) is divisible by d whenever (a mod d) + (b mod d) = kd.