Suppose A and B are both divisible by M. Prove that A^2-B^2 is divisible by M.

Question

Suppose A and B are both divisible by M. Prove that A^2-B^2  is divisible by M.

perl · Answer

A is divisible by M :
 A= M*k, k is some integer 
B is divisible by M: 
B = M*h , h is some integer
Now 
A^2 - B^2
=  (M*k)^2 - (M*h)^2 
= M^2*k^2 - M^2*h^2
= M^2 * (k^2 - h^2) 
= M * [M(k^2-h^2)]

so A^2 - B^2 = M*(some integer)

therefore A^2 - B^2 is divisible by M

perl · Answer

you can make a stronger statement, A^2 - B^2 is divisible by M^2

anonymous · Answer

or you could say if A is divisible by M and B is divisible by M then also $A-B$ is divisible by M  and $A+B$ is as well