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Let aaa and bbb be relatively prime positive integers. Find the sum of all possible values of
gcd(a2017+b2017a+b, a+b).\gcd \left(\frac{a^{2017} + b^{2017}}{a + b}, \ a + b \right).gcd(a+ba2017+b2017, a+b).
Note: 2017 is prime.
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