Divide a A3 document in two A4 documents

Surprisingly simple:

sudo apt install pdfposter
pdfposter -s1 a3-input.pdf a4-output.pdf

pdfposter defaults to output to A4 by default (see man pdfposter for other options). All we have to do is tell it not to scale (with -s1) and it'll figure things out for itself.

Note that you'll need a printer that can print right up to the edges.