A threshold gate implementing a linear threshold function on $n$ boolean inputs $x_1, x_2 \ldots, x_n$ is given by the equation: $w_1 x_1 + w_2 x_2 + \ldots, w_n x_n \ge t$ where $w_1, \ldots, w_n, t \in \mathbb{R}$. The $w_i$'s are called the weights of the threshold function and $t$ is called the threshold, and naturally, the gate fires a $1$ on an input $x$ if the weighted sum given by the equation above exceeds $t$.
Now, almost everywhere in the literature on threshold circuits, I encounter this fact (which I am guessing, is folklore since I couldn't find a proof anywhere): The $w_i$'s in the linear equation above can be made integers (on $n \log{n}$ bits), and a threshold circuit made up of these gates will still compute whatever was possible with real weights. I have given this some thought, and I think it must be a simple trick, but I have failed to obtain a proof of this fact. Can somebody help or provide me with a reference? (the only reference I could find was a text by Muroga, which I couldn't procure)