MathDB

BMO Shortlist 2021 N4

Source: BMO Shortlist 2021

May 8, 2022

Balkanshortlist2021number theory

Problem Statement

Can every positive rational number

q

be written as

\frac{a^{2021} + b^{2023}}{c^{2022} + d^{2024}},

where

a, b, c, d

are all positive integers?
Proposed by Dominic Yeo, UK