Find the error with this proof and explain how it mat be corrected in order to clearly prove the equation.
prove that if m is an odd integer, then m2 is odd.
proposed proof: assume m is an odd integer. by definition of odd integer, m=2k+1, for some integer k.
this means that (2k + 1)^2 = 4k^2 + 1, so m is odd.

Step-by-step explanation:

It is true that for any given odd integer, square of that integer will also be odd.

i.e if is and odd integer then is also odd.

In the given proof the expansion for is incorrect.

By definition we know,

∴

Now, we know and will be even values

∴ will be odd

hence will be odd, which means will be odd.