MathDB

Inequalities regarding integers

Source: 2018 Taiwan TST Round 3

April 2, 2020

inequalitiesTaiwan

Problem Statement

Suppose that

x,y

are distinct positive reals, and

n>1

is a positive integer. If

x^n-y^n=x^{n+1}-y^{n+1},

then show that

1<x+y<\frac{2n}{n+1}.