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if 0 <\sqrt {2002} - \frac {a}{b} <\frac {\lambda}{ab}, prove \lambda \geq 5

Source: Rioplatense Olympiad 2002 level 3 P2

January 8, 2019
InequalityIntegerspositive integersnumber theoryalgebra

Problem Statement

Let λ\lambda be a real number such that the inequality 0<2002−ab<λab0 <\sqrt {2002} - \frac {a} {b} <\frac {\lambda} {ab} holds for an infinite number of pairs (a,b) (a, b) of positive integers. Prove that λ≥5\lambda \geq 5 .
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