MathDB

2017 Guts #20

Source:

November 25, 2022

2017Guts Round

Problem Statement

Let

\alpha

and

\beta

be positive rational numbers so that

\alpha+\beta\sqrt{5}

is a root of some polynomial

x^2+ax+b

where

a

and

b

are integers. What is the smallest possible value of

\alpha\beta