Find all pairs of integers (x, y) such that x^3+y^3=(x+y)^2. Math Olympiad Challenges

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This video explains how to find all pairs of integers (x, y) such that x^3+y^3=(x+y)^2. Firstly, by rearranging and simplifying the original equation, solving the equation is converted to solving one linear equation and one quadratic equation in x. Secondly, as both x and y are integers, therefore, the discriminant of the quadratic equation must be greater than or equal to zero, from which the range of y can be determined. Finally, all x values can be found by substituting each value of y in the original equation.

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Nice video, for x^2-xy+y^2-x-y=0, we can get (x-y)^2+(x-1)^2+(y-1)^2=2, from which we can derive the solutions.

edwardedward

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