SOLUTION: solve : x^2 + x = y^2 - 2y , x, y belong to N (integer)

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Question 1141463: solve : x^2 + x = y^2 - 2y , x, y belong to N (integer)
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


x%5E2%2Bx+=+y%5E2-2y
x%28x%2B1%29+=+y%28y-2%29
x%28x%2B1%29-y%28y-2%29+=+0

The equation is satisfied when x(x+1) and y(y-2) are both 0:

(1) x=0 and y=0;
(2) x=0 and y=2;
(3) x=-1 and y=0; and
(4) x=-1 and y=2

Solutions: (0,0), (0,2), (-1,0), (-1,2)

That does not preclude the possibility of other solutions; it seems unlikely that there would be.

Entering "integer solutions to x^2+x=y^2-2y on wolframalpha.com shows only those four solutions.