Algebra Level 5

Find the sum of all positive integers $$(a,b)$$ such that

$\small{\small{\sqrt{\dfrac{(-a+b+\sqrt{a^2+b^2})(a-b+\sqrt{a^2+b^2})(a+b-\sqrt{a^2+b^2})}{4}\sqrt{\dfrac{(-a+b+\sqrt{a^2+b^2})(a-b+\sqrt{a^2+b^2})(a+b-\sqrt{a^2+b^2})}{4}\sqrt{\dots\dots}}}=4(a+b+\sqrt{a^2+b^2})}}.$

Details and Assumptions

• $$(a,b)$$ is same as $$(b,a)$$, no need to add twice.
• This is inspired by Mursalin Habib.
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