4 integers wanted in a trinomial
Source: Austria Beginners' Competition 2011 p2
October 3, 2021
algebraquadratics
Problem Statement
Let and be real numbers. The quadratic equation
has the real solutions and . In addition, the following two conditions apply:
(i) The numbers and differ from each other by exactly .
(ii) The numbers and differ from each other by exactly .
Show that then , , and are integers.(G. Kirchner, University of Innsbruck)