MathDB

Finite number of triples with given properties

Source: German Mathematical Competition BWM 2005, 2nd round, problem

September 1, 2005

algebra proposedalgebra

Problem Statement

Let be

x

a rational number. Prove: There are only finitely many triples

(a,b,c)

of integers with

a<0

and

b^2-4ac=5

such that

ax^2+bx+c

is positive.