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x^2+5y^2-6\leq \sqrt{(x^2-2)(y^2-0.04)} integers

Source: 2004 Austria Beginners' Competition p2

October 4, 2022
number theoryinequalitiesdiophantine

Problem Statement

For what pairs of integers (x,y)(x,y) does the inequality x2+5y2−6≤(x2−2)(y2−0.04)x^2+5y^2-6\leq \sqrt{(x^2-2)(y^2-0.04)} hold?
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