2. Reduce to absurdity. Suppose there is an equation in which m and n satisfy. (m+n)(m-n)=4(k- 1)+2

To make the equation hold, m is even, n is odd, or n is even, m is odd, and the left and right sides of the equation are odd, which cannot hold.

If m and n are even numbers, the left is a multiple of 4, the right is divided by 4, and the remainder is 2, the equation cannot be established.

If both m and n are odd numbers, the left is a multiple of 4, the right is divided by 4, and the remainder is 2, the equation cannot be established.

So there are no integers m and n that satisfy the equation.