Question 500817
Pretty straightforward. If t divides a and t divides b, then a &#8801; 0 (mod t) and b &#8801; 0 (mod t). Then we can multiply a and b by integers and the residue is still 0 mod t (i.e. ax &#8801; 0, by &#8801; 0). Then we can add them and we obtain our desired result, ax + by &#8801; 0 (mod t) <--> t divides ax + by.