Hello,

I came up with a conjecture regarding squarefree integers of the form $\displaystyle x^2 + 1$. My conjecture is :

**Note** : each prime in the prime factorization of a squarefree number only comes up once. For instance, $\displaystyle 2^2 \times 3$ is not squarefree while $\displaystyle 5^1 \times 11^1$ is.

I'm not absolutely sure it holds but I'm pretty confident, so I've been trying to prove it using an inductive step but I hardly see how to do it because as I try to do it (check its divisibility by the square of all prime numbers one after the other, and by some routine process show that it cannot be divided by it) it involves two variables which is obviously wrong ... perhaps someone here has an idea and could help me out on this one, give hints to get me started, put me on the right track (or you can just disprove the conjecture

).