MathDB

2008 ToT Spring Junior A P6 a/b + c/d = 1, a/d + c/b = 2008

Source:

March 7, 2020

number theorysystem of equations

Problem Statement

Do there exist positive integers

a,b,c

and

d

such that

\begin{cases} \dfrac{a}{b} + \dfrac{c}{d} = 1\\ \\ \dfrac{a}{d} + \dfrac{c}{b} = 2008\end{cases}