SOLUTION: find all ordered pairs of integers (x, y) such that : x^3 = 89x+40y y^3 = 89x+40y

Question 1110336: find all ordered pairs of integers (x, y) such that :
x^3 = 89x+40y
y^3 = 89x+40y
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
.

1.  Right sides are identical  ====>  hence, left sides are equal:

    x^3 = y^3.


2.  Since x and y are integer, the last equality implies  x = y.


3.  Then the either of the two given equations is equivalent to

    x^3 = 89x + 40x,   or

    x^3 = 129x,

    x*(x^2-129) = 0.


    In integer numbers, the last equation has only one solution  x= 0.



Answer.  The only solution to the original system in integer numbers is the pair (x,y) = (0,0).

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