MathDB

mutually exclusive sets and coprimality

Source: Serbia MO 2006 2nd Grade P3

April 10, 2021

number theory

Problem Statement

For every natural number

a

, consider the set

S(a)=\{a^n+a+1|n=2,3,\ldots\}

. Does there exist an infinite set

A\subset\mathbb N

with the property that for any two distinct elements

x,y\in A

x

and

y

are coprime and

S(x)\cap S(y)=\emptyset