I was asked two questions related to Diophantine equations.
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Can one find all integer triplets $(x,y,z)$ satisfying $x^2 + x = y^2 + y + z^2 + z$? I mean some kind of parametrization which gives all solutions but no points which do not satisfy the equation.
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Is there an algorithm that will determine, given any quadratic $Q(x_1,\ldots,x_n)$ as input, all integer points of this quadratic? In the case of existence of solution, there is an algorithm, https://math.stackexchange.com/questions/181380/second-degree-diophantine-equations/181384#comment418090_181384