I've been trying to understand the proof for a solution to the Euler 9 problem. I'm on this site under the heading "Solving the problem". I've understood the parts that came before it (excluding the "proof" )
[IMO, reading the project euler problem is not necessary to understand what's happening below]
I'm specifically wondering how the author concluded that since $m|(s/2)\implies m<\sqrt{s/2}$. I mean, even $12$ divides $48$ but $12>\sqrt(48)\approx 7$.
What am I missing here?
$s=2m(m+n)d \implies s/2=m(m+n)d>m^2$ so $\color{blue}{m<\sqrt {s/2}}$
Also, $s/2=m(m+n)d \implies \color{blue}{m \mid s/2}$
So those are two outcomes of the given equation, not derived from each other (in either direction).