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Multiply both sides by $a^4b^4$, $$ a^4b^4( a+ b)(a x+ b)(a y+ b)(a z+ b )- a^4b^4=0.$$Įquate the coefficients of $a^4b^4=0$, obtain a system of 4 linear equations in $a$ and $b$. I think I’ve got a few ideas, but none of them seem to work and I’m quite stuck. This is a practice question from my textbook, and I’m not exactly sure how to go about it. Has three solutions in integers x, y, and z.

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