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Problems for Chapter V
Problems for Chapter V
1. If we permit polynomials with arbitrary complex coefficients and
ask the “Waring” problem for polynomials, then show that x is
not the sum of 2 cubes, but it is the sum of 3 cubes.
2. Show that every polynomial is the sum of 3 cubes.
3. Show, in general, that the polynomial x is “pivotal,” that is if x is
the sum of gnth powers, then every polynomial is the sum of g
nth powers.

4. Show that if max(z, b) > 2c, where c is the degree of R(x), then
b
a
P + Q R is unsolvable.
5. Show that the constant polynomial 1 can be written as the sum of
√
4n + 1 nth powers of nonconstant polynomials.