### Abstract

Let q be a power of a prime number. Observe that just for q ε {3,9} some congruence obstructions occur to the representation of polynomials in F_{q}[t] as a sum (and so also as a strict sum) of biquadrates. We define g(4,F_{q}[t}) as the least g such that every polynomial that is a strict sum of biquadrates is a strict sum of g biquadrates. We compare the set of sums of biquadrates with the set of strict sums of biquadrates for q ε {3,9}. Our main result is that g(4,F_{q}[t]) ≤14 when q ε {3,9}. The set of sums of cubes in F_{4}[t] is also determined. This completes the study of the case of representation by sums of cubes (in which the congruence obstructions occur only for 9 ε{2,4}).

Original language | English (US) |
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Pages (from-to) | 1863-1874 |

Number of pages | 12 |

Journal | Rocky Mountain Journal of Mathematics |

Volume | 40 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1 2010 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

_{q}[t],qε{3,9}.

*Rocky Mountain Journal of Mathematics*,

*40*(6), 1863-1874. https://doi.org/10.1216/RMJ-2010-40-6-1863