Question: > 
> I would like a **hint and only a hint** to prove
> 
> 
> $\forall \sigma\in S\_n$ , $S\_n$ is a finite symmetric group of permutation
> 
> 
> $\displaystyle \left|\prod\limits\_{1\le i<j\le n}\big(\sigma(i)-\sigma(j)\big)\right|=\left|\prod\limits\_{1\le i<j\le n}\big(i-j\big)\right|$
> 
> 
> 

thanks !!

Answer: 
HINT: try by induction, starting from $n=2$
Here is another: prove their squares are equal, both being $\prod\_{i\neq j} (i-j)$.