B. Mishra

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math.NT2024

Polynomials with factors of the form $(x^{q} - a)$ with roots modulo every integer

Bhawesh Mishra

Given an odd prime $q$ , a natural number $l$ and non-zero $q$ -free integers $a_{1}, a_{2}, \dots, a_{l}$ , none of which are equal to $1$ or $- 1$ , we give necessary and sufficient…

math.NT2023

Almost No Finite Subset of Integers Contains a $q^{t h}$ Power Modulo Almost Every Prime

Bhawesh Mishra

Let $q$ be a prime. We give an elementary proof of the fact that for any $k \in N$ , the proportion of $k$ -element subsets of $Z$ that contain a $q^{t h}$ power modul…

math.NT2023

Prime Power Residue and Linear Coverings of Vector Space over $F_{q}$

Bhawesh Mishra

Let $q$ be an odd prime and $B = {b_{j}}_{j = 1}^{l}$ be a finite set of nonzero integers that does not contain a perfect $q^{t h}$ power. We show that $B$ has a $q^{t h}$ power modu…

Polynomials with factors of the form (xq−a) with roots modulo every integer

Almost No Finite Subset of Integers Contains a qth Power Modulo Almost Every Prime

Prime Power Residue and Linear Coverings of Vector Space over Fq​

Polynomials with factors of the form $(x^{q} - a)$ with roots modulo every integer

Almost No Finite Subset of Integers Contains a $q^{t h}$ Power Modulo Almost Every Prime

Prime Power Residue and Linear Coverings of Vector Space over $F_{q}$