MathDB

We say that a subset

T

\{1, 2, \dots, 2024\}

is kawaii if

T

has the following properties: 1.

T

has at least two distinct elements; 2. For any two distinct elements

x

and

y

T

x - y

does not divide

x + y

.
For example, the subset

T = \{31, 71, 2024\}

is kawaii, but

T = \{5, 15, 75\}

is not kawaii because

15 - 5 = 10

divides

15 + 5 = 20

.
What is the largest possible number of elements that a kawaii subset can have?

Problem Statement