Additive polynomial
= Additive polynomial
{title2=$L(X+Y)=L(X)+L(Y)$}
{wiki}
Over a <field> of characteristic $p$, additive <polynomials> are sums of $p$-power monomials, $L(X)=\sum_i a_iX^{p^i}$. They act linearly over the prime <field>. The identity follows from the <Frobenius endomorphism>; the converse follows by comparing mixed binomial coefficients. Their zero sets are additive groups, and a nonzero linear coefficient makes all roots simple.