Erdős Problem #496 — Approximating an irrational multiple by a Pythagorean form

For every irrational real $α$ and every $ε>0$ , do there exist integers $x,y,z$ such that $|x^2+y^2-αz^2|<ε$ ?

References

Primary source

P. Erdős, Some unsolved problems, A Magyar Tudományos Akadémia Matematikai Kutató Intézetének Közleményei 6 (1961), 221–254.

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