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For which integer values of $a$ and $b$ is the following equation true?

$$ \sqrt { a^{ 2 }+b^{ 2 } } =a+b$$

Always

For all positive values of $a$ and $b$ only

For all nonnegative values of $a$ and $b$ only

Only when $a = 0$ or $b = 0$ (but not both)

Only when $a = 0$ and $b = 0$