MathDB
Miklos Schweitzer 1952_4

Source:

October 12, 2008
algebrapolynomialsuperior algebrasuperior algebra unsolved

Problem Statement

Let K K be a finite field of p p elements, where p p is a prime. For every polynomial f(x)\equal{}\sum_{i\equal{}0}^na_ix^i (∈K[x] \in 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)\in K[x], f(x)‾∣g(x)‾ \overline{f(x)}|\overline{g(x)} if and only if f(x)∣g(x) f(x)|g(x).
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