Respuesta :
Let's say we start with the odd number 3.
Squaring it leads to 3^2 = 3*3 = 9
Dividing that by 2 yields 9/2 = 4.5 which is not a whole number. This counterexample shows that the original statement is false.
We only need one counterexample because the original statement implies that it works for all odd numbers, but we just show it doesn't work for 3.
-------------
Here's another example:
Start with 7. It squares to 7^2 = 49 and then cuts in half to 49/2 = 24.5 showing that we get another non-whole result here as well.
-------------
It turns out that you can pick any odd number you want, square it, cut it in half, and you won't ever get a whole number result. So there isn't anything special about the choices of 3 and 7.
