D. Basnet

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20242026

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math.NT2024

Existence of Special Types Primitive Pairs in Finite Fields Avoiding Affine Hyperplanes

Himangshu Hazarika, Giorgos Kapetanakis, Dhiren Kumar Basnet

Let $\Fm$ be finite fields of order $q^{m}$ , where $m \geq 2$ and $q$ , a prime power. Given $\F$-affine hyperplanes $A_{1}, \dots, A_{m}$ of $\Fm$ in general position, we study the existe…

math.NT2024

Primitive pairs of rational functions with prescribed traces over finite fields

Shikhamoni Nath, Dhiren Kumar Basnet

Let $q$ be a positive integral power of some prime $p$ and $F_{q^{m}}$ be a finite field with $q^{m}$ elements for some $m \in N$ . Here we establish a sufficient cond…

math.NT2024

Primitive normal pairs with prescribed traces over finite fields

Shikhamoni Nath, Arpan Chandra Mazumder, Dhiren Kumar Basnet

Let $q$ be a positive integral power of some prime $p$ and $F_{q^{m}}$ be a finite field with $q^{m}$ elements for some $m \in N$ . Here we establish a sufficient cond…

math.NT2024

Primitive normal pairs of elements with one prescribed trace

Arpan Chandra Mazumder, Himangshu Hazarika, Dhiren Kumar Basnet +1

Let $q, n, m \in N$ such that $q$ is a prime power, $m \geq 3$ and $a \in F$ . We establish a sufficient condition for the existence of a primitive normal pair ($Î…

math.NT2024

On existence of primitive normal elements of rational form over finite fields of even characteristic

Himangshu Hazarika, Dhiren Kumar Basnet, Giorgos Kapetanakis

Let $q$ be an even prime power and $m \geq 2$ an integer. By $F_{q}$ , we denote the finite field of order $q$ and by $F_{q^{m}}$ its extension degree $m$ . In this paper…

math.NT2024

Idempotents of $Z_{n}$

Suman Mondal, Dhiren Kumar Basnet

We know that if there are $k$ distinct prime factors of $n \in N$ , then the ring $Z_{n}$ of integers modulo $n$ has exactly $2^{k}$ idempotent elements. In this artic…

Existence of Special Types Primitive Pairs in Finite Fields Avoiding Affine Hyperplanes

Primitive pairs of rational functions with prescribed traces over finite fields

Primitive normal pairs with prescribed traces over finite fields

Primitive normal pairs of elements with one prescribed trace

On existence of primitive normal elements of rational form over finite fields of even characteristic

Idempotents of Zn​

Idempotents of $Z_{n}$