Cut out Cubes

How many pairs of integers ( x , y ) (x,y) satisfy the equation x 3 + y 3 = 13094193293 ? x^3+y^3=13094193293\; ?

1 4 6 3 5 2 0

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1 solution

Relevant wiki: Fermat's Last Theorem

First of all, 13094193293 = 235 7 3 13094193293=2357^3 .

Therefore, by Fermat's Last Theorem, it is clear that there are no solutions in x , y > 0 x,y > 0 . However, allowing one of x , y x,y to be zero, there are two trivial solutions. ( x , y ) = ( 2357 , 0 ) , ( 0 , 2357 ) (x,y)=(2357,0),(0,2357) .

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