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Keywords:
Sidon set; additive basis; polynomial rings over finite fields
Sidon set; additive basis; polynomial rings over finite fields
Summary:
Let $\mathbb {F}_q[t]$ denote the polynomial ring over $\mathbb {F}_q$, the finite field of $q$ elements. Suppose the characteristic of $\mathbb {F}_q$ is not $2$ or $3$. We prove that there exist infinitely many $N \in \mathbb {N}$ such that the set $\{ f \in \mathbb {F}_q[t] \colon \deg f < N \}$ contains a Sidon set which is an additive basis of order $3$.
References:
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