EVERY POLYNOMIAL OVER A FIELD CONTAINING 𝔽16 IS A STRICT SUM OF FOUR CUBES AND ONE EXPRESSION A2 + A

Title & Authors
EVERY POLYNOMIAL OVER A FIELD CONTAINING 𝔽16 IS A STRICT SUM OF FOUR CUBES AND ONE EXPRESSION A2 + A
Gallardo, Luis H.;

Abstract
Let q be a power of 16. Every polynomial $\small{P\in\mathbb{F}_q}$[t] is a strict sum $P Keywords Waring`s problem;quadratic polynomials;cubes;finite fields;characteristic 2; Language English Cited by References 1. E. Artin, Geometric Algebra, Wiley (Interscience), 1957 2. L. H. Gallardo, On the restricted Waring problem over$F_2n$[t], Acta Arith. 92 (2000), no. 2, 109–113 3. L. H. Gallardo, Waring's problem for cubes and squares over a finite field of even characteristic, Bull. Belg. Math. Soc. Simon Stevin 12 (2005), no. 3, 349–362 4. L. H. Gallardo, Every strict sum of cubes in$F_4$[t] is a strict sum of 6 cubes, Port. Math. 65 (2008), no. 2, 227–236 5. L. H. Gallardo and D. R. Heath-Brown, Every sum of cubes in$F_2$[t] is a strict sum of 6 cubes, Finite Fields Appl. 13 (2007), no. 4, 981–987 6. L. H. Gallardo, O. Rahavandrainy, and L. Vaserstein, Representations of polynomials over finite fields of characteristic two as$A^2+A+BC+D^3\$, Finite Fields Appl. 13 (2007), no. 3, 648–658

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