Question

Prove that the characteristics of finite field is always prime.

Answer 1

Step-by-step explanation:

So, for some distinct i and j, the sum of i 1s must equal the sum of j 1s and by subtraction the sum of ( i -j ) 1s must equal 0. The smallest number of 1s that sum to 0 is called the characteristics of the finite field, and the characteristic mist be a prime number.