Can you prove that if n is a perfect square, then n+2 is not a perfect square?

perfect-square

#1

Can you prove that if n is a perfect square, then n+2 is not a perfect square?

Answer:

you can prove it by contradiction: so suppose that n is a perfect square say n=k^2 (where k is an integer) and suppose also that n+2 is a perfect square, meaning there is an integer m such that n+2=m^2. by replacing n by its value we get k^2+2=m^2.
we conclude that k^2-m^2=2. this equivalent to (k-m)(k+m)=2. Try to find the possible value of k and m and derive and contradiction