MathDB

Sqrt(x^2 + y^3) and sqrt(x^3 + y^2) are rational

Source: BWM 2004, 2nd round, problem 4

September 1, 2004

number theory proposednumber theory

Problem Statement

Prove that there exist infinitely many pairs

\left(x;\;y\right)

of different positive rational numbers, such that the numbers

\sqrt{x^2+y^3}

and

\sqrt{x^3+y^2}

are both rational.