If you want to find out which package contains a particular file, you can use apt-file. If you want to search archives for a different architecture, you have to use the -a option, first to create/update the cache for that architecture (normal updating only creates/updates the default one) and then when searching. You can try:
sudo apt-file -a i386 update
apt-file -a i386 search /lib/i386-linux-gnu/libgmp.so.3
This should tell you the correct package to install. If the i386 isn't enabled for you system, you will have to enable it. You should be able to check with:
dpkg --print-foreign-architectures
If i386 isn't listed, you can add it with:
sudo dpkg --add-architecture i386
The above should work for newer Ubuntu versions, but for older ones you might have to do:
sudo dpkg --foreign-architecture i386
After adding, update the package lists:
sudo apt-get update
Then you should be able to install the package found from your apt-file search like this:
sudo apt-get install libwhatever:i386
If apt-file doesn't find anything, then it could mean that the library installs to a different place. You could try:
apt-file -a i386 search libgmp.so.3
Then install whatever package it finds. If you do this and you program still doesn't work, you could try symlinking /lib/i386-linux-gnu/libgmp.so.3 to wherever it does install to. Otherwise, if apt-file doesn't find anything, it likely means that there is no package which contains that version of the library in the repositories. You could then look for a package from a different version of Mint/Ubuntu (or the backports for your release may be a good place to start looking if the release's version is older). If you are really stuck, you would have to cross-compile and install from source.
Update
Your apt-file output, shows your distro libgmp package is libgmp10 which contains libgmp.so.10. Since you are looking for libgmp.so.3, there is no prizes for guessing this is an older version. No point looking in backports, since this is for newer packages.
A search on http://packages.ubuntu.com/ shows there is a libgmp3 in Ubuntu 12.04. The package page with links to the list of files is here - http://packages.ubuntu.com/precise/libgmp3c2. Installing the 32 bit package on 64 bit Ubuntu/Mint will put the files in different places though (ie libraries in /lib/i386-linux-gnu. You can download it here - http://packages.ubuntu.com/precise/i386/libgmp3c2/download
Usually this is can be problematic due to possible conflicts, but since the package has a different name it shouldn't conflict with any current libgmp. It also has only one dependency on libc6 which is the same as what is in Ubuntu 13.04 (the base for Olivia). There will be a different minor version, which may cause some odd bugs, but most likely you will be ok.
You can install like:
sudo dpkg -i dir/downloaded_package.deb
You may also have to install the i386 version of libc6 if you don't have it already:
sudo apt-get install libc6:i386
.i686or something similar. I'm not familiar with Mint, sorry. – vonbrand Mar 15 '14 at 17:38ldd. But without knowing the correct package to install, I do not see how your comment is useful. Can you elaborate? – Ole Tange Mar 16 '14 at 10:53