Hi Everybody,

First of all thank you for your time.

Is it know when the next identity holds?
$
A^s-B^s=(A-B)^s
$

$
A, B, s \in Z$

Links with more resources on this identity would be grateful

Thank you a lot

2. In a field with characteristic p it is true that
$(a+b)^p=a^p+b^p$, you just use the binomial formula to see why all the cross terms cancel out. For instance $\mathbb{Z}_p$ is an example of a field of characteristic p.

3. Yes sorry,
This was a little bit dummy question, the actual issue was

$
|\frac{(A-B)^s}{A^s-B^s}| \leq 1
$

$
A,B,s \in \mathbb{Z}
$

Which this is obvious for any A,B and for s>1

Anyway thank you