MathDB

3

Part of 2019 Singapore Senior Math Olympiad

Problems(1)

Pairwise LCMs greater than 4000

Source: SMO Senior 2019 Q3

6/29/2019
Let a1,a2,⋯ ,a2000a_1,a_2,\cdots,a_{2000} be distinct positive integers such that 1≤a1<a2<⋯<a2000<40001 \leq a_1 < a_2 < \cdots < a_{2000} < 4000 such that the LCM (least common multiple) of any two of them is ≥4000\geq 4000. Show that a1≥1334a_1 \geq 1334
number theoryleast common multiple