# Go Factor!

Number Theory Level 5

$\large 399\:337 = 616^2 + 141^2 \\ \large 399\:337 = 464^2 + 429^2$ The number $$399\:337$$ is the product of two prime numbers $$p\times q$$. Determine these prime numbers without using a calculator.

Submit your answer as the sum $$p + q$$.

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