1

Part of 2022 Miklós Schweitzer

Problems(1)

Existence of some defined infinite irregular set

Source: 2022 Miklós Schweitzer Problem 1

We say that a set

A \subset \mathbb Z

is irregular if, for any different elements

x, y \in A

, there is no element of the form

x + k(y -x)

x

y

k

is an integer). Is there an infinite irregular set?

real analysiscollege contestscombinatoricsMiklos Schweitzer