#### Chandrasekhar Hall

#### x^n + x + a

#### V Kumar Murty

##### University of Toronto

*This family of polynomials has many nice properties. In*

particular, we will discuss their irreducibility, their discriminants,

and their Galois groups, and why they are relevant in coding theory

and in cryptography. There are many interesting open problems about the

prime divisors of the discriminants. I will describe joint work with

undergraduate student Shuyang Shen on some of these questions in which we

explore consequences of the ABC conjecture.

Done