MathDB

a,b in N: x^2+ax-b , x^2-ax+b have integer roots, existence of a right triangle

Source: INAMO Shortlist 2015 N2

May 14, 2019

trinomialarea of a trianglealgebrainteger rootright triangleIntegers

Problem Statement

Suppose that

a, b

are natural numbers so that all the roots of

x^2 + ax - b

and

x^2 - ax + b

are integers. Show that exists a right triangle with integer sides, with

a

the length of the hypotenuse and

b

the area .