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AUSTRIAN-POLISH 2005 Problem 9

    Consider the equation x3+y3+z3=2x^3 + y^3 + z^3 = 2 . a) Prove that it has infinitely many integer solutions x,y,zx,y,z . b) Determine all integer solutions x,y,zx, y, z with ∣x∣,∣y∣,∣z∣≤28|x|, |y|, |z| \leq 28 .

    Dataset text AI-MO AoPS. Quoted with source.

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