On a curious property of 3435

TL;DR

The paper explores the interesting property of the number 3435, demonstrating it as a Munchausen number in base 10 and establishing the finiteness of such numbers across all bases.

Contribution

It introduces the concept of Munchausen numbers, proves 3435's property as one, and shows that only finitely many such numbers exist in any given base.

Findings

3435 is a Munchausen number in base 10

Finitely many Munchausen numbers exist in each base

The paper formalizes the concept of Munchausen numbers

Abstract

Folklore tells us that there are no uninteresting natural numbers. But some natural numbers are more interesting then others. In this article we will explain why 3435 is one of the more interesting natural numbers around. We will show that 3435 is a Munchausen number in base 10, and we will explain what we mean by that. We will further show that for every base there are finitely many Munchausen numbers in that base.