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x^2 +y^2 = a^2 +b^2, x^3 +y^3 = a^3 +b^3, x,y,a,b>0

Source: 1982 Polish MO Finals p3

February 25, 2020

system of equationsparameteralgebra

Problem Statement

Find all pairs of positive numbers

(x,y)

which satisfy the system of equations

\begin{cases} x^2 +y^2 = a^2 +b^2 \\ x^3 +y^3 = a^3 +b^3 \end{cases}

where

a

and

b

are given positive numbers.