4

Part of 1982 Spain Mathematical Olympiad

Problems(1)

p(|z|) <= x^4 + y^4 where z=x + iy , p(0) = 0

Source: Spanish Mathematical Olympiad 1981 P4

Determine a polynomial of non-negative real coefficients that satisfies the following two conditions:

p(0) = 0, p(|z|) \le x^4 + y^4,

|z|

the module of the complex number

z = x + iy

complex numberspolynomialalgebrainequalities