Let \(N=2^k\times4^m\times8^n\)where \(k,m,n\) are positive whole numbers. Then \(N\) will definitely be a square number whenever

\(k\) is even;

\(k+n\) is odd;

\(k\) is odd but \(m+n\) is even;

\(k+n\) is even.

When is a number a square? How else can we write the factors to help us?