Got dam 47

What the title is referencing

The Brilli military has established a number of dams on Pluto to collect water, since they heard that there is ice on Pluto . However, anti-Brilli forces have captured Dam Number 47 and will not release it unless it receives G dollars or the members of Brilliant.org answer this math problem.

The positive integer solutions to the equation x 2 + 47 = y 3 x^2+47=y^3 can be written are ( x 1 , y 1 ) , (x_1,y_1), ( x 2 , y 2 ) , (x_2,y_2), and ( x 3 , y 3 ) . (x_3,y_3). Find x 1 + x 2 + x 3 + y 1 + y 2 + y 3 . x_1+x_2+x_3+y_1+y_2+y_3.


The answer is 635.

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