Bigness (Part 2)

In the 1980s, the mathematician Ronald Graham asked if its possible to color each positive integer either red or blue, so that no triple of integers obeying Pythagoras famous equation:

all have the same color. He offered a prize of $100.

Its was solved in 2016! The answer is no. You can do it for numbers up to 7824, and a solution is shown here:

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(White squares can go either way.)

But you cant do it for numbers up to 7825. To prove this, you could try all the ways of coloring these...