# Thread: Freshman's Dream Subtraction Version? (a-b)^p = a^p - b^p ?

1. ## Freshman's Dream Subtraction Version? (a-b)^p = a^p - b^p ?

Hello All,

I am trying to prove the insolvability of quintics, and I am now working on finite fields.

I have proved Freshman's dream (a+b)^p = a^p + b^p for field with char = p, and that is obvious.

However, I have seen a couple of authors use (a-b)^p = a^p - b^p in some of the proofs for finite fields. While p is odd, this is certainly right, but what if p = 2? How can this subtraction version of Freshman's dream be true in general?

Thanks!!!

Regards,
Bosco

2. Originally Posted by boscomanilow128
Hello All,

I am trying to prove the insolvability of quintics, and I am now working on finite fields.

I have proved Freshman's dream (a+b)^p = a^p + b^p for field with char = p, and that is obvious.

However, I have seen a couple of authors use (a-b)^p = a^p - b^p in some of the proofs for finite fields. While p is odd, this is certainly right, but what if p = 2? How can this subtraction version of Freshman's dream be true in general?

Thanks!!!

Regards,
Bosco
Abel-Ruffini proved that long time ago!