Hi Everybody, First of all thank you for your time. Is it know when the next identity holds? $\displaystyle A^s-B^s=(A-B)^s $ $\displaystyle A, B, s \in Z$ Links with more resources on this identity would be grateful Thank you a lot
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In a field with characteristic p it is true that $\displaystyle (a+b)^p=a^p+b^p$, you just use the binomial formula to see why all the cross terms cancel out. For instance $\displaystyle \mathbb{Z}_p$ is an example of a field of characteristic p.
Yes sorry, This was a little bit dummy question, the actual issue was $\displaystyle |\frac{(A-B)^s}{A^s-B^s}| \leq 1 $ $\displaystyle A,B,s \in \mathbb{Z} $ Which this is obvious for any A,B and for s>1 Anyway thank you
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