Is it possible to determine when $$4a^2+4b^2+4a+4b+1 = ((2a+2b)+1)^2-8ab = (2a+1)^2+4(b^2+b)$$ is a perfect square, assuming $a,b \in \mathbb{Z}$ and $b>0$? I've tried writing it in a few different forms but I'm not sure if there's a strategy to approach this.
2026-04-03 06:20:51.1775197251
When is $4a^2+4b^2+4a+4b+1$ a square?
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