MathDB

Decimal functions in binary

Source: India TST 2023 Day 3 P1

July 9, 2023

number theory

Problem Statement

Let

\mathbb{N}

be the set of all positive integers. Find all functions

f : \mathbb{N} \rightarrow \mathbb{N}

such that

f(x) + y

and

f(y) + x

have the same number of

1

's in their binary representations, for any

x,y \in \mathbb{N}