When will $N$ definitely be a square number?

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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

1. \(k\) is even;

2. \(k+n\) is odd;

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

4. \(k+n\) is even.

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