Question 80
A number is called cool if it is the sum of two nonnegative perfect squares. For example the numbers $17$ and $25$ are cool because $17=4^{2}+1^{2}$ and $25=5^{2}+0^{2}$, but the number $15$ is not cool.
Show that if $k$ is cool, then $2k$ is cool.
Show that if $k$ is cool, then $2k$ is cool.