Sums of biquadrates and cubes in F-q[t]

摘要

Every polynomial P is an element of F-q [t] where gcd (q, 6) = 1 and q is not an element of {5, 13, 17, 25, 29}, is a strict mixed sum of 11 biquadrates and it is also a strict sum of 16 biquadrates. For the strict mixed sum representation, a supplementary biquadrate is required for q is an element of {13, 17, 25, 29} and four supplementary biquadrates for q = 5. Every polynomial P is an element of F-q[t] where gcd (q, 6) = I and q is not an element of {7,13} is a strict sum of 7 cubes. One supplementary cube is required for q = 13 and two for q = 7. [References: 10]