MathDB

Alan is assigning values to lattice points on the 3d coordinate plane. First, Alan computes the roots of the cubic

20x^3-22x^2+2x+1

and finds that they are

\alpha

\beta

, and

\gamma

. He finds out that each of these roots satisfy

|\alpha|,|\beta|,|\gamma|\leq 1

On each point

(x,y,z)

where

x,y,

and

z

are all nonnegative integers, Alan writes down

\alpha^x\beta^y\gamma^z

. What is the value of the sum of all numbers he writes down?
Proposed by Alan Abraham

Problem Statement