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MathNet 2024-part-04 — 168 problems (EN–VI) Question 102

Math Olympiad Vault · MathNet 2024-part-04 — 168 problems (EN–VI)

Question 102

Find all the real numbers $x$ and $y$ so that:
(i) $x \ge 2y^2$;
(ii) $y \ge 2x^2$;
(iii) the number $8(x - y)$ is an integer.