MathDB

Indian RMO - Paper -4[4]

Source:

December 12, 2013

Problem Statement

Let

x

be a non-zero real numbers such that

x^4+\frac{1}{x^4}

and

x^5+\frac{1}{x^5}

are both rational numbers. Prove that

x+\frac{1}{x}

is a rational number.