Can you find a simple proof for this statement?
I thought more about the last question I added into the addendum of the Numberphile, Graph theory and Mathematica post
It can be succinctly stated as:
such that and .
For all integers m, greater than 19, there are two other distinct positive integers less than m such that the sum of each with m, when square rooted is an integer.
What is the shortest proof you can find for this statement?