When I used to run a Bitcoin node on my Raspberry Pi2, I used to download from Source and build it. This used to take a lot of time to build but eventually completed. To speed up the process I used to get the blockchain synchronized on my desktop PC into my external hard disk and then connect it to my raspberry pi. This way it would not require the RAM or resource needed for initial full blockchain synchronization. Also make sure you create some swap memory if needed for the build (not sure if this is needed for the pi 3).
So what you need to do first is to create a directory anywhere you'd like on your raspberry pi (if needed do it in your MicroSD card) and then clone Bitcoin core's git repo and then do the following:
sudo apt-get update
sudo apt-get upgrade [This will update and upgrade all packages on your raspbian OS (considering that you're using this OS)
Then install all dependencies (if you had 0.13x) maybe it was already installed, but just do it to verify
sudo apt-get install autoconf libevent-dev libtool libssl-dev libboost-all-dev libminiupnpc-dev qt4-dev-tools libprotobuf-dev protobuf-compiler libqrencode-dev -y
I suggest you follow the instructions here for the dependencies if needed for QT5:
https://github.com/bitcoin/bitcoin/blob/master/doc/build-unix.mdAlso install Berkeley DB (maybe it's also already installed for you) if not you'll need to build it [Also note, if the dependencies above do install berkeley db, then maybe this isn't required, I can't recall so well but I'm placing the steps below just incase].
mkdir ~/bin
cd ~/bin
wget http://download.oracle.com/berkeley-db/db-4.8.30.NC.tar.gz
tar -xzvf db-4.8.30.NC.tar.gz
cd db-4.8.30.NC/build_unix/
../dist/configure --enable-cxx
make -j2 (You can also try -j4 which may be quicker, but at times the build used to fail for me)
sudo make install
Alternatively you can also follow how to build Berkeley DB here if needed:
https://github.com/bitcoin/bitcoin/blob/master/doc/build-unix.mdNow you clone the git repo, before that do
sudo apt-get install git
to install git.
git clone -b v0.15.1 https://github.com/bitcoin/bitcoin.git
After which, run the following in the bitcoin folder to build (Remember this will take a lot of time on the raspberry pi:
./autogen.sh
./configure CPPFLAGS="-I/usr/local/BerkeleyDB.4.8/include -O2" LDFLAGS="-L/usr/local/BerkeleyDB.4.8/lib" --disable-wallet (use --disable-wallet only if you want to run the node without a wallet enabled in it)
make -j2
sudo make install
After which you can run
bitcoin-qt
I'm not sure since it's been long, but maybe you can also try download the 64 bit linux build from
https://bitcoin.org/bin/bitcoin-core-0.15.1/ and then run bitcoin-qt, might work as well instead of building from scratch.