MathDB

Rationals/irrationals

Source: INMO 1998 Prolem 2

October 6, 2005

quadraticsalgebranumber theory solvednumber theory

Problem Statement

Let

a

and

b

be two positive rational numbers such that

\sqrt[3] {a} + \sqrt[3]{b}

is also a rational number. Prove that

\sqrt[3]{a}

and

\sqrt[3] {b}

themselves are rational numbers.