Let there be $131$ given distinct natural numbers, each having prime divisors not exceeding $42$. Prove that one can choose four of them whose product is a perfect square.
Source: Mongolian MO 2002 Grade 10 P4
Tags: number theory
Let there be $131$ given distinct natural numbers, each having prime divisors not exceeding $42$. Prove that one can choose four of them whose product is a perfect square.