1. The problem statement, all variables and given/known data proove is either true of false let A be a set of integer closed under subtraction. if x and y are element of A, then x-ny is in A for any n in Z. 2. Relevant equations n/a 3. The attempt at a solution is there any proof, without induction? i suspect its true because any arbitrary positive integer n will satisfy, though if i try using induction also i stuck. when n=0, satisfied, assume it is true for some n>=0 x-(n+1)y=(x-ny)-y, clearly it is inside A let n>0 x-(-n)y and i don't know how to continue now, anyway, help me with this induction and also what are other ways without using proof by induction?