Question

Prove that the difference between between squares of consecutive even number is always a multiple of 4. Let n stand for any integer in your working.

Answer 1

2n and 2n+2 are two consecutive even numbers, then the difference of their squares is:

• (2n+2)²- (2n)²= (2n+2+2n)(2n+2-2n)= (4n+2)*2= 2*(2n+1)*2= 4*(2n+1)

As we see it is multiple of 4.