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How we can find the all pairs $(x,y)$ from the integers numbers ,that satisfy the equation :

$$xy+\frac{x^3+y^3}{3} =2007$$

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    Are you familiar with the factorization of $a^3 + b^3 + c^3 - 3abc$? (This is not a terribly well-known factorization.)2012-08-30
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    @QiaochuYuan, are you saying $x^3+y^3+(-1)^3-3xy(-1)=(x+y-1)(x^2+y^2+1-xy+x+y)$? Could you please elaborate a bit?2012-08-30
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    @Qiaochu Yuan can you elaborate a bit more , please ?2017-03-26

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