Mint 17 is based on Ubuntu trusty and hence you can follow the instruction given below to install ROS-Indigo:
http://answers.ros.org/question/190177/how-to-install-ros-indigo-in-ubuntu-1404-trusty-64-bit/
However, you need to make slight change in the name of repository to be added to your sources.list. The summary of instruction is as follows:
$ sudo sh -c '. /etc/lsb-release && echo "deb http://mirror.umd.edu/packages.ros.org/ros/ubuntu trusty main" > /etc/apt/sources.list.d/ros-latest.list'
http://answers.ros.org/question/190177/how-to-install-ros-indigo-in-ubuntu-1404-trusty-64-bit/
However, you need to make slight change in the name of repository to be added to your sources.list. The summary of instruction is as follows:
$ sudo sh -c '. /etc/lsb-release && echo "deb http://mirror.umd.edu/packages.ros.org/ros/ubuntu trusty main" > /etc/apt/sources.list.d/ros-latest.list'
$ wget https://raw.githubusercontent.com/ros/rosdistro/master/ros.key -O - | sudo apt-key add -
$ sudo apt-get update
$ sudo apt-get install ros-indigo-desktop-full
Basically replace $DISTRIB_CODENAME by 'trusty'. It is because the $DISTRIB_CODENAME for mint 17 is 'qiana' for which its 404 error.