Are Euclid numbers squarefree ? An Euclid number is by definition a Primorial number + 1. See http://mathworld.wolfram.com/Primorial.html.
In notation the $n$ th Euclid number is written as $E_n = P_n+1.$
Thus I wonder about $a^2b = E_n$ for positive integer $a,b,n$ and $a>1$.
I was thinking about Korselt's criterion : http://mathworld.wolfram.com/KorseltsCriterion.html and Fermats little.
Im unaware of other techniques for proving the squarefree property apart from more elementary tools as gcd and basic modular aritmetic.
I cannot imagine infinite descent to work here ? Maybe a binomium will help ?
I guess I missed something trivial and have a bad day.
Maybe $a^2b = E_n-2$ is easier ?