For four pairwise different positive integers $a,b,c$ and $d$ six numbers are calculated: $ab+10$,$ac+10$,$ad+10$,$bc+10$,$bd+10$ and $cd+10$. Find the maximum amount of them which can be perfect squares.
Source: Belarusian National Olympiad 2021
Tags: number theory
For four pairwise different positive integers $a,b,c$ and $d$ six numbers are calculated: $ab+10$,$ac+10$,$ad+10$,$bc+10$,$bd+10$ and $cd+10$. Find the maximum amount of them which can be perfect squares.