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|ka + lb + mc| > 1/h

Source: China TST 1996, problem 6

May 17, 2005
complex numbersalgebra unsolvedalgebra

Problem Statement

Does there exist non-zero complex numbers a,b,ca, b, c and natural number hh such that if integers k,l,mk, l, m satisfy ∣k∣+∣l∣+∣m∣≥1996|k| + |l| + |m| \geq 1996, then ∣ka+lb+mc∣>1h|ka + lb + mc| > \frac {1}{h} is true?
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