Theorem 1 (Freshman’s dream).
The theorem is so named because it is a common mistake for freshman math students to make over the real numbers. However, as the characteristic of the real numbers is 0, this does not apply in any interesting way to that setting.
It should also be noted that the result applies only to powers of the characteristic, and not all exponents.
The proof is an application of the binomial theorem. We prove it for first.
As is prime and it follows and do not divide . As the field has characteristic , is an integer where
Now for simply use induction:
|Date of creation||2013-03-22 15:51:17|
|Last modified on||2013-03-22 15:51:17|
|Last modified by||Algeboy (12884)|