Change JPG images to fit into an A4 PDF page

Hello,

I have a bunch of JPEG files that I want to convert into PDFs. They
all have different aspect ratios and sizes, but every file should
end up perfectly fitted into an A4 sized PDF (without borders). If
I just use

convert in.jpg -page A4 out.odf

many of the pages end up being either too large or small because the
density isn't correct i most of the files. What I want to do is:

* First add some white borders at the top and bottom or left and
  right so that the aspect ratio is like an A4 page.
* Only change the density in the image (don't actually resize it) so
  that it actually represents and A4 sized page.

Is this all possible with "convert"?

Sebastian