15
votes
3answers
1k views
$\prod_{n=1}^{\infty} n{}^{\mu(n)}=\frac{1}{4 \pi ^2}$
When I tested this in Mathematica, I had expected it to say it did not converge. However, I got this:
$$\prod_{n=1}^{\infty} n{}^{\mu(n)}=\frac{1}{4 \pi ^2}$$
This indicates t …
10
votes
5answers
986 views
are there infinitely many triples of consecutive square-free integers?
The title says it all ... Obviously, any such triple must be of the form
$(4a+1,4a+2,4a+3)$ where $a$ is an integer. Has this problem
already been studied before ? The result would …
4
votes
1answer
380 views
Integer polynomial (of degree >1) all of whose values are square-free
Is there an integer polynomial $ A \in {\mathbb Z} [ X ]$ of degree $d\geq 2$ such that for any integer $n\in {\mathbb Z}$ , $ A(n) $ is a square-free integer?
