Examples
The polynomial xp is additive. Indeed, for any a and b in the algebraic closure of k one has by the binomial theorem
Since p is prime, for all n = 1, ..., p−1 the binomial coefficient is divisible by p, which implies that
as polynomials in a and b.
Similarly all the polynomials of the form
are additive, where n is a non-negative integer.
Read more about this topic: Additive Polynomial
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