Challenge: sum of squares. Let's break 299

[Allen]

I think I may have found a general solution to this problem.
As a test case I picked 4 numbers over 299 and got solutions for all 4: 300,310, 400,487

The un-optimized code is than 30 lines of python and finishes in a few min on a single CPU, near-linear time, lear linear memory requirements.

Before I post code and comments, I would be grateful if someone could verify my solution #487.