Sam's Mistake

Algebra Level 4

Sam is excited to learn about the distributive law, and thinks that it applies to every possible operation. As such, he claims that a2+b2=a2+b2\sqrt{a^2 + b^2} = \sqrt{a^2} + \sqrt{b^2}

How many ordered pairs of integers (a,b(a, b) are there, such that 10a10,10b10-10≤a≤10, -10≤b≤10 and a2+b2=a2+b2?\sqrt{a^2 + b^2} = \sqrt{a^2} + \sqrt{b^2}?

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