Numberphile's Square-Sum Problem was solved!

Breaking Math News! The "Square-Sum problem" by Matt Parker/Numberphile was solved! Let's explore HOW it was solved and how we could have stumbled upon its solution.

Link to the original video:    • The Square-Sum Problem - Numberphile  
Book by Matt Parker: Things to Make and Do in the Fourth Dimension

The proof was given by Robert Gerbicz and posted in an online forum https://www.mersenneforum.org/showthr... . All main results of this video are based on this work. Some details that are left out here were answered in this forum.

If you are experienced in the programming language C/C++, Robert Gerbicz included a program squares.c that generates solutions for the Square-Sum Problem for arbitrarily large n less than 2^63. In its source code are all the initial "Ninja Pairs" given as well as the 49*2=98 ways to construct new "Ninja Pairs".