$2d^2=n^2$ implies that $n$ is multiple of 2 I'm reading a proof of the irrationality of $\sqrt 2$. In a step it states that $2d^2=n^2$ implies that $n$ is multiple of 2. How?
$\;2\;$ is a prime and divides the left side in $\,2d^2=n^2\;$ ,
 so by the fundamental theorem of arithmetic it also divides the right hand side...
square of even numbers are even, so $n$ is even