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Linear and Quadratic Square (Posted on 20150315) 

Each of A and B is a positive integer with gcd(A,B) =1 such that each of
A^{2} + 2*B^{2} and A + 2*B is a perfect square.
What is the smallest value of A + 2*B for which this is possible? Determine the next two smallest values of A+2*B that satisfy the given conditions.
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