From square to square

Number Theory Level 3

$\begin{array} { c c c r } 259^2 & + & 319^2 & = &168 \: 842 \\ a^2 & + & b^2 & = &84 \: 421 \\ \end{array}$

Assuming $$a$$ and $$b$$ are positive integers, find $$a + b$$.

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