Write down careful proofs of the following statements:

(a) \(\sqrt{6}-\sqrt{2}>1\).

(b) If \(n\) is an integer such that \(n^{2}\) is even, then \(n\) is even.

(c) If \(n=m^{3}-m\) for some integer \(m\), then \(n\) is a multiple of 6 .