Biswajit Koley

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math.NT2020

Irreducibility of $x^{n} - a$

Biswajit Koley, A. Satyanarayana Reddy

A. Capelli gave a necessary and sufficient condition for the reducibility of $x^{n} - a$ over $\Q$. In this article, we are providing an alternate elementary proof for the same.

math.NT2020

An irreducible class of polynomials over integers

Biswajit Koley, A. Satyanarayana Reddy

In this article, we consider polynomials of the form $f (x) = a_{0} + a_{n_{1}} x^{n_{1}} + a_{n_{2}} x^{n_{2}} + \dots + a_{n_{r}} x^{n_{r}} \in Z [x],$ where $∣ a_{0} ∣ \geq ∣ a_{n_{1}} ∣ + \dots + ∣ a_{n_{r}} ∣,$ $|a…

math.NT2019

Irreducibility criterion for certain trinomials

Biswajit Koley, A. Satyanarayana Reddy

In this article we study the irreducibility of polynomials of the form $x^{n} + ε_{1} x^{m} + p^{k} ε_{2}$ , $p$ being a prime number. We will show that they are irreducible for $m = 1$ . We have als…

math.NT2019

An irreducibility criterion for polynomials over integers

Biswajit Koley, A. Satyanarayana Reddy

In this article, we consider the polynomials of the form $f (x) = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{n} x^{n} \in Z [x],$ where $∣ a_{0} ∣ = ∣ a_{1} ∣ + \dots + ∣ a_{n} ∣$ and $∣ a_{0} ∣$ is a prime. We show that…

Irreducibility of xn−a

An irreducible class of polynomials over integers

Irreducibility criterion for certain trinomials

An irreducibility criterion for polynomials over integers

Irreducibility of $x^{n} - a$