Quadratic eqns
Source: INMO 1995 Problem 2
October 6, 2005
quadraticsnumber theoryrelatively primeDiophantine equationalgebra unsolvedalgebra
Problem Statement
Show that there are infintely many pairs of relatively prime integers (not necessarily positive) such that both the equations \begin{eqnarray*} x^2 +ax +b &=& 0 \\ x^2 + 2ax + b &=& 0 \\ \end{eqnarray*} have integer roots.