2

Part of 2002 Rioplatense Mathematical Olympiad, Level 3

Problems(1)

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

Source: Rioplatense Olympiad 2002 level 3 P2

\lambda

be a real number such that the inequality

0 <\sqrt {2002} - \frac {a} {b} <\frac {\lambda} {ab}

holds for an infinite number of pairs

(a, b)

of positive integers. Prove that

\lambda \geq 5

InequalityIntegerspositive integersnumber theoryalgebra