<s>[INST] The square of any odd integer is odd. Suppose that $n$ is an odd integer. Then $n = 2k + 1$ for some integer $k$. 
Hence $n^2=(2k+1)(2k+1)=4k^2+4k+1=2(2k^2+2k)+1$.
Since $k$ is an integer, $2k^2 + 2k$ is an integer. Thus $n^2 = 2k' + 1$ for some integer $k'$.
Therefore $n^2$ is odd.
Is this correct?
 [/INST] you can write more generally that the product of 2 odd integers is odd
let $a = 2k+1$ and $b = 2p+1$
then $ab = (2k+1)(2p+1) = 2(2kp+k+p)+1 $ which is the general format of odd numbers
</s>