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Omni-MATH / Determine, with proof, whether there exist positive integers x and y such that x+y,x²+y², and x³+y³ are all perfect squares.

Problem

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problem

Determine, with proof, whether there exist positive integers xx and yy such that x+y,x2+y2x+y, x^{2}+y^{2}, and x3+y3x^{3}+y^{3} are all perfect squares.
Plain-text mathematical notation (without MathML)
Determine, with proof, whether there exist positive integers x and y such that x+y,x²+y², and x³+y³ are all perfect squares.
Original LaTeX notation
Determine, with proof, whether there exist positive integers $x$ and $y$ such that $x+y, x^{2}+y^{2}$, and $x^{3}+y^{3}$ are all perfect squares.

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Source and history

task_id
2e2a8bd2-3157-56e3-afec-9ef542623911
task_key
test--2e2a8bd2-3157-56e3-afec-9ef542623911
task_revision_id
1
config / split
/ test

Official source

initial import