Survey on irreducibility of trinomials

TL;DR

This survey reviews various criteria for determining when trinomials with integer coefficients are irreducible over the rationals, providing a comprehensive overview of existing methods.

Contribution

It compiles and analyzes existing irreducibility criteria for trinomials, offering a valuable reference for researchers in algebra and number theory.

Findings

Summarizes key irreducibility criteria for trinomials

Identifies gaps and open problems in current criteria

Provides a structured overview of the field

Abstract

Let $a,b,c$ be non-zero integers and $f(x)=ax^n+bx^m+c$ be a trinomial of degree $n$. We surveyed the irreducibility criteria of $f(x)$ over rational numbers.