It is proved that when n is an integer, the square of the square difference (2n + 1) of two consecutive odd numbers is a multiple of 8

It is proved that when n is an integer, the square of the square difference (2n + 1) of two consecutive odd numbers is a multiple of 8

Square of (2n + 1) - (2n-1)
=4N^2+1+4N-4N^2-1+4N
=8N
Because n is an integer, 8N is a multiple of 8
That is to say, the square of the square difference (2n + 1) of two consecutive odd numbers is a multiple of 8