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x^3+y^3+z^3=2

Source: Austrian-Polish 2005, Problem 9

July 5, 2015
number theoryDiophantine equationsum of cubesinfinitely many solutions

Problem Statement

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.
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