Let K be a finite field of p elements, where p is a prime. For every polynomial
f(x)\equal{}\sum_{i\equal{}0}^na_ix^i (∈K[x])
put
\overline{f(x)}\equal{}\sum_{i\equal{}0}^n a_ix^{p^i}.
Prove that for any pair of polynomials f(x),g(x)∈K[x], f(x)∣g(x) if and only if f(x)∣g(x). algebrapolynomialsuperior algebrasuperior algebra unsolved