Suppose f is a finite field. (a) prove that there exists a smallest positive integer n such that 1 + 1+ +1 (n terms) is the additive identity 0. the integer n is called the characteristic of the field. (b) prove that if n is the characteristic of f, then for each a € f, ata ++a (n terms) is 0. (c) prove that the characteristic of a finite field must be a prime number. (hint: suppose n = kl, where 1