Geodesic
Sidon basis in polynomial rings over finite fields
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 2, pp. 555-562
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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 $3$.
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 $3$.
DOI : 10.21136/CMJ.2020.0543-19
Classification : 11B83, 11K31, 11T55
Keywords: Sidon set; additive basis; polynomial rings over finite fields 
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Kuo, Wentang; Yamagishi, Shuntaro. Sidon basis in polynomial rings over finite fields. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 2, pp. 555-562. doi: 10.21136/CMJ.2020.0543-19

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