Question 178
Let's call a positive integer square-free, if it's not divisible by $p^2$ for any prime $p$. You are given a squarefree integer $n \gt 1$, which has precisely $d$ positive divisors. What largest number of divisors of this number can you choose, so that for any two of them, let's denote them by $a$ and $b$, the number $a^2 + ab - n$ isn't a square of an integer?
(Oleksii Masalitin)
(Oleksii Masalitin)