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
Famous quotes containing the word examples:
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)