MathDB

N2

Part of 2015 Indonesia MO Shortlist

Problems(1)

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

5/14/2019
Suppose that a,ba, b are natural numbers so that all the roots of x2+ax−bx^2 + ax - b and x2−ax+bx^2 - ax + b are integers. Show that exists a right triangle with integer sides, with aa the length of the hypotenuse and bb the area .
trinomialarea of a trianglealgebrainteger rootright triangleIntegers