2

Part of 2011 Danube Mathematical Competition

Problems(1)

2- Donova Mathematical Olympiad 2011 ( Romania)

Source: DMO11

Let S be a set of positive integers such that: min { lcm (x, y) : x, y ∈ S,

x \neq y

\ge

2 + max S. Prove that

\displaystyle\sum\limits_{x \in S} \frac{1}{x} \le \frac{3}{2}

number theoryleast common multiplenumber theory unsolved